Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #15667984 |
| commutator, cosocle | C42×C89 | C23 |
| Frattini | C42 | C22×D89 |
| Fitting | #459×C89 | C2 |
| socle | C22×C89 | #121 |
| hypercenter | #459 | D89 |
| hypocenter | C89 | #1687 |
| LCS | G ▷ C42×C89 ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19151974 | C2 | semidirect |
| 2. #19151793 | C2 | semidirect |
| 3. #19151676 | C2 | semidirect |
| 4. #19151348 | C2 | semidirect |
| 5. #19151342 | C2 | semidirect |
| 6. #19151341 | C2 | semidirect |
| 7. #459×C89 | C2 | semidirect |
| 69. #10623494 | D8 | semidirect |
| 93. C89 | #1687 | semidirect |
| 96. #459 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151974 | 2 |
| #19151793 | 2 |
| #19151676 | 2 |
| #19151348 | 2 |
| #19151342 | 2 |
| #19151341 | 2 |
| #459×C89 | 2 |
| #1687 | 89 |