Finite Group DatabasebetaFinite Group DatabasebetaOrder 36752.
10 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C8×C2297 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×C2297 | C4 | 1 | 1 | yes | characteristic |
| 3 | C2×C2297 | C8 | 1 | 1 | yes | characteristic |
| 4 | C2297 | C16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 5 | C16 | — | 2297 | 1 | no | maximal, Sylow |
| 6 | C8 | D2297 | 1 | 1 | yes | characteristic |
| 7 | C4 | Dic2297 | 1 | 1 | yes | characteristic |
| 8 | C2 | #32913587 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D2297 |
| commutator, hypocenter | C2297 | C16 |
| Fitting, cosocle | C8×C2297 | C2 |
| socle, prime radical | C2×C2297 | C8 |
| LCS | G ▷ C2297 | |
| UCS | C1 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2297 | C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C2297 | 2 |
| C16 | 2297 |