Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
924 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 201 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 | C2×#121×C181 | C2 |
| hypercenter | C2×#121 | D181 |
| hypocenter | C181 | #2856 |
| LCS | G ▷ C23×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19153812 | C2 | semidirect |
| 2. C2×#19153790 | C2 | semidirect |
| 3. C2×#19153788 | C2 | semidirect |
| 4. C22×C4×Dic181 | C2 | semidirect |
| 5. #26041182 | C2 | semidirect |
| 6. #26041180 | C2 | semidirect |
| 7. #26041179 | C2 | semidirect |
| 8. #26041148 | C2 | semidirect |
| 9. C2×#121×C181 | C2 | semidirect |
| 43. C22×Dic181 | D4 | semidirect |
| 54. C4×Dic181 | D4 | semidirect |
| 64. C22×C4×C181 | D4 | semidirect |
| 118. C22×C181 | #127 | semidirect |
| 131. C4×C181 | #121 | semidirect |
| 134. Dic181 | #121 | semidirect |
| 143. C181 | #2856 | semidirect |
| 148. C2×#121 | D181 | semidirect |
| 200. C22×C4 | C22⋊D181 | semidirect |
| 267. C22 | #19153812 | semidirect |
| 278. C4 | #19153788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153812 | 2 |
| C2×#19153790 | 2 |
| C2×#19153788 | 2 |
| C22×C4×Dic181 | 2 |
| #26041182 | 2 |
| #26041180 | 2 |
| #26041179 | 2 |
| #26041148 | 2 |
| C2×#121×C181 | 2 |
| #2856 | 181 |