Finite Group DatabasebetaFinite Group DatabasebetaOrder 27028.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D6757 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C29×C233 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #11745400 | — | 29 | 1 | no | maximal, Hall |
| 4 | D233 | — | 29 | 1 | no | — |
| 5 | C233 | #1181 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | #1181 | — | 233 | 1 | no | maximal, Hall |
| 7 | D29 | — | 233 | 1 | no | — |
| 8 | C29 | #11745400 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C4 | — | 6757 | 1 | no | Sylow |
| 10 | C2 | — | 6757 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C233 | C4 |
| prime radical, cosocle | D6757 | C2 |
| LCS | G ▷ C29×C233 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×C233 | C4 | semidirect |
| 5. C233 | #1181 | semidirect |
| 8. C29 | #11745400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D6757 | 2 |
| #11745400 | 29 |
| #1181 | 233 |