Finite Group DatabasebetaFinite Group DatabasebetaOrder 2028.
36 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#92789 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10621725 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | #92789 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C2×C132 | C2×C3 | 1 | 1 | yes | characteristic |
| 5 | C132 | C3×C4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | Dic13⋊C3 | — | 13 | 2 | no | maximal |
| 7 | C2×C13⋊C3 | — | 13 | 2 | no | — |
| 8 | Dic13 | — | 13 | 2 | no | — |
| 9 | Dic13 | — | 39 | 4 | no | — |
| 10 | C13⋊C3 | — | 13 | 2 | no | — |
| 11 | C2×C13 | — | 3 | 4 | no | — |
| 12 | C2×C13 | D13⋊C3 | 1 | 2 | yes | — |
| 13 | C13 | — | 3 | 4 | no | — |
| 14 | C13 | Dic13⋊C3 | 1 | 2 | yes | complemented |
| 15 | C3×C4 | — | 169 | 1 | no | Hall |
| 16 | C2×C3 | — | 169 | 1 | no | — |
| 17 | C4 | — | 169 | 1 | no | Sylow |
| 18 | C3 | — | 169 | 1 | no | Sylow |
| 19 | C2 | #11759816 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #11759816 |
| commutator, hypocenter | C132 | C3×C4 |
| Fitting, socle, cosocle | C2×C132 | C2×C3 |
| prime radical | C2×#92789 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10621725 | C3 | semidirect |
| 3. #92789 | C4 | semidirect |
| 5. C132 | C3×C4 | semidirect |
| 14. C13 | Dic13⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92789 | 2 |
| #10621725 | 3 |
| Dic13⋊C3 | 13 |