Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 173 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×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | C2×#127×C89 | C2 |
| hypercenter | C2×#127 | D89 |
| hypocenter | C89 | #2431 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#13083573 | C2 | semidirect |
| 2. C2×#15667999 | C2 | semidirect |
| 3. C2×#15667983 | C2 | semidirect |
| 4. #19151506 | C2 | semidirect |
| 5. #19151504 | C2 | semidirect |
| 6. #19151501 | C2 | semidirect |
| 7. #19151478 | C2 | semidirect |
| 8. C4×#13083551 | C2 | semidirect |
| 9. C2×#127×C89 | C2 | semidirect |
| 37. C2×Dic178 | D4 | semidirect |
| 52. C2×C4×D89 | D4 | semidirect |
| 69. C2×D4×C89 | D4 | semidirect |
| 97. C2×C4×C89 | #41 | semidirect |
| 149. C89 | #2431 | semidirect |
| 151. C2×#127 | D89 | semidirect |
| 202. C2×D4 | C22⋊D89 | semidirect |
| 262. C2×C4 | #13083573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083573 | 2 |
| C2×#15667999 | 2 |
| C2×#15667983 | 2 |
| #19151506 | 2 |
| #19151504 | 2 |
| #19151501 | 2 |
| #19151478 | 2 |
| C4×#13083551 | 2 |
| C2×#127×C89 | 2 |
| #2431 | 89 |