Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668044 | C2 | semidirect |
| 2. #19152260 | C2 | semidirect |
| 3. #19151982 | C2 | semidirect |
| 4. #19151845 | C2 | semidirect |
| 5. #19151820 | C2 | semidirect |
| 6. #19151755 | C2 | semidirect |
| 7. #19151746 | C2 | semidirect |
| 8. #19151677 | C2 | semidirect |
| 9. C4×Q16×C89 | C2 | semidirect |
| 64. Q16×C89 | D4 | semidirect |
| 118. C89 | #3277 | semidirect |
| 126. C4×Q16 | D89 | semidirect |
| 170. Q16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668044 | 2 |
| #19152260 | 2 |
| #19151982 | 2 |
| #19151845 | 2 |
| #19151820 | 2 |
| #19151755 | 2 |
| #19151746 | 2 |
| #19151677 | 2 |
| C4×Q16×C89 | 2 |
| #3277 | 89 |