Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 115 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 | #395×C181 | C2 |
| prime radical | C23×D181 | C23 |
| hypercenter | #395 | D181 |
| hypocenter | C181 | #2835 |
| LCS | G ▷ C23×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26041220 | C2 | semidirect |
| 2. #26041217 | C2 | semidirect |
| 4. #26041198 | C2 | semidirect |
| 7. #395×C181 | C2 | semidirect |
| 70. C181 | #2835 | semidirect |
| 76. #395 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041220 | 2 |
| #26041217 | 2 |
| #26041208 | 2 |
| #26041198 | 2 |
| #26041190 | 2 |
| #26041150 | 2 |
| #395×C181 | 2 |
| #2835 | 181 |