Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
760 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C4×C4⋊C4×C89 | C2 |
| hypercenter | C4×C4⋊C4 | D89 |
| hypocenter | C89 | #2540 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668000 | C2 | semidirect |
| 2. C2×#15667992 | C2 | semidirect |
| 3. C2×#15667987 | C2 | semidirect |
| 4. C2×C4×D356 | C2 | semidirect |
| 5. #19151535 | C2 | semidirect |
| 6. #19151508 | C2 | semidirect |
| 7. #19151500 | C2 | semidirect |
| 8. C4×C4⋊C4×C89 | C2 | semidirect |
| 56. C4⋊C4×C89 | D4 | semidirect |
| 58. C42×C89 | D4 | semidirect |
| 123. C89 | #2540 | semidirect |
| 131. C4×C4⋊C4 | D89 | semidirect |
| 174. C4⋊C4 | D356 | semidirect |
| 181. C42 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668000 | 2 |
| C2×#15667992 | 2 |
| C2×#15667987 | 2 |
| C2×C4×D356 | 2 |
| #19151535 | 2 |
| #19151508 | 2 |
| #19151500 | 2 |
| C4×C4⋊C4×C89 | 2 |
| #2540 | 89 |