Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1068 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1068 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 | #380×C181 | C2 |
| prime radical | C24×D181 | C22 |
| hypercenter | #380 | D181 |
| hypocenter | C181 | #2848 |
| LCS | G ▷ C23×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19153796 | C2 | semidirect |
| 3. C2×#19153795 | C2 | semidirect |
| 4. #26041154 | C2 | semidirect |
| 5. #26041153 | C2 | semidirect |
| 6. #26041136 | C2 | semidirect |
| 8. #380×C181 | C2 | semidirect |
| 10. C22×Dic362 | C22 | semidirect |
| 18. C2×C4⋊Dic181 | C22 | semidirect |
| 19. C2×C4⋊Dic181 | C22 | semidirect |
| 20. C2×#15668428 | C22 | semidirect |
| 24. #19153723 | C22 | semidirect |
| 26. C2×C4⋊C4×C181 | C22 | semidirect |
| 28. #95×C181 | C22 | semidirect |
| 33. C23×D181 | Q8 | semidirect |
| 104. C22×C181 | C22⋊Q8 | semidirect |
| 117. C2×D181 | C22⋊Q8 | semidirect |
| 131. C181 | #2848 | semidirect |
| 139. #380 | D181 | semidirect |
| 154. C2×C4⋊C4 | C2×D181 | semidirect |
| 160. #95 | C2×D181 | semidirect |
| 244. C22 | #19153796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D181 | 2 |
| C2×#19153796 | 2 |
| C2×#19153795 | 2 |
| #26041154 | 2 |
| #26041153 | 2 |
| #26041136 | 2 |
| #26041134 | 2 |
| #380×C181 | 2 |
| #2848 | 181 |