Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
914 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 914 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×#95×C89 | C2 |
| hypercenter | C2×#95 | D89 |
| hypocenter | C89 | #2430 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#13083574 | C2 | semidirect |
| 2. C2×#15667995 | C2 | semidirect |
| 3. C2×#15667986 | C2 | semidirect |
| 4. #19151519 | C2 | semidirect |
| 5. #19151516 | C2 | semidirect |
| 6. #19151511 | C2 | semidirect |
| 7. #19151508 | C2 | semidirect |
| 8. #19151477 | C2 | semidirect |
| 9. #19151476 | C2 | semidirect |
| 10. #19151472 | C2 | semidirect |
| 11. C2×#95×C89 | C2 | semidirect |
| 53. C2×C22⋊D89 | D4 | semidirect |
| 76. C22×C4×C89 | D4 | semidirect |
| 110. C2×C4×C89 | #41 | semidirect |
| 166. C89 | #2430 | semidirect |
| 177. C2×#95 | D89 | semidirect |
| 232. C22×C4 | D356 | semidirect |
| 292. C2×C4 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083574 | 2 |
| C2×#15667995 | 2 |
| C2×#15667986 | 2 |
| #19151519 | 2 |
| #19151516 | 2 |
| #19151511 | 2 |
| #19151508 | 2 |
| #19151477 | 2 |
| #19151476 | 2 |
| #19151472 | 2 |
| C2×#95×C89 | 2 |
| #2430 | 89 |