Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D181 |
| commutator, socle, cosocle | C23×C181 | C24 |
| Fitting | #391×C181 | C2 |
| prime radical | C22×D724 | C22 |
| hypercenter | #391 | D181 |
| hypocenter | C181 | #2861 |
| LCS | G ▷ C23×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19153807 | C2 | semidirect |
| 3. #26041186 | C2 | semidirect |
| 6. #26041171 | C2 | semidirect |
| 7. #26041168 | C2 | semidirect |
| 8. C42×Dic181 | C2 | semidirect |
| 9. #391×C181 | C2 | semidirect |
| 109. C181 | #2861 | semidirect |
| 114. #391 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153807 | 2 |
| C2×#19153805 | 2 |
| #26041186 | 2 |
| #26041181 | 2 |
| #26041180 | 2 |
| #26041171 | 2 |
| #26041168 | 2 |
| C42×Dic181 | 2 |
| #391×C181 | 2 |
| #2861 | 181 |