Finite Group DatabasebetaFinite Group DatabasebetaOrder 31974.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5329⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D5329 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C5329 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 4 | D73⋊C3 | — | 73 | 1 | no | maximal |
| 5 | C73⋊C3 | — | 73 | 1 | no | — |
| 6 | D73 | — | 73 | 1 | no | — |
| 7 | C73 | D73⋊C3 | 1 | 1 | yes | characteristic |
| 8 | C2×C3 | — | 5329 | 1 | no | Hall |
| 9 | C3 | — | 5329 | 1 | no | Sylow |
| 10 | C2 | — | 5329 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5329 | C2×C3 |
| Frattini, socle | C73 | D73⋊C3 |
| LCS | G ▷ C5329 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5329⋊C3 | C2 | semidirect |
| 2. D5329 | C3 | semidirect |
| 3. C5329 | C2×C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5329⋊C3 | 2 |
| D5329 | 3 |
| D73⋊C3 | 73 |