Finite Group DatabasebetaFinite Group DatabasebetaOrder 32412.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #30633769 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #24925160 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | #22549193 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C73×D37 | C2×C3 | 1 | 1 | yes | characteristic |
| 5 | C37×C73 | C3×C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | Dic73⋊C3 | — | 37 | 1 | no | maximal, Hall |
| 7 | #3866⋊C3 | — | 73 | 1 | no | maximal, Hall |
| 8 | C2×C73⋊C3 | — | 37 | 1 | no | — |
| 9 | Dic73 | — | 37 | 1 | no | Hall |
| 10 | D37⋊C3 | — | 73 | 1 | no | — |
| 11 | C73⋊C3 | — | 37 | 1 | no | Hall |
| 12 | #3866 | — | 73 | 1 | no | Hall |
| 13 | C2×C73 | — | 37 | 1 | no | — |
| 14 | C37⋊C3 | — | 73 | 1 | no | Hall |
| 15 | D37 | D73⋊C3 | 1 | 1 | yes | characteristic |
| 16 | C73 | #3866⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 17 | C37 | Dic73⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 18 | C3×C4 | — | 2701 | 1 | no | Hall |
| 19 | C2×C3 | — | 2701 | 1 | no | — |
| 20 | C4 | — | 2701 | 1 | no | Sylow |
| 21 | C3 | — | 2701 | 1 | no | Sylow |
| 22 | C2 | — | 37 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C73 | C3×C4 |
| prime radical | #30633769 | C2 |
| cosocle | C73×D37 | C2×C3 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #24925160 | C3 | semidirect |
| 3. #22549193 | C4 | semidirect |
| 5. C37×C73 | C3×C4 | semidirect |
| 16. C73 | #3866⋊C3 | semidirect |
| 17. C37 | Dic73⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30633769 | 2 |
| #24925160 | 3 |
| Dic73⋊C3 | 37 |
| #3866⋊C3 | 73 |