Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #19151706 | C2 | semidirect |
| 4. #19151705 | C2 | semidirect |
| 5. #19151704 | C2 | semidirect |
| 6. C4×#13083564 | C2 | semidirect |
| 7. #19151690 | C2 | semidirect |
| 11. #441×C89 | C2 | semidirect |
| 15. Q16×D89 | C4 | semidirect |
| 109. C89 | #2950 | semidirect |
| 115. #441 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D89 | 2 |
| #19152074 | 2 |
| #19151706 | 2 |
| #19151705 | 2 |
| #19151704 | 2 |
| C4×#13083564 | 2 |
| #19151690 | 2 |
| #19151633 | 2 |
| #19151605 | 2 |
| #19151555 | 2 |
| #441×C89 | 2 |
| #2950 | 89 |