Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#15668043 | C2 | semidirect |
| 3. #19152172 | C2 | semidirect |
| 4. #19151779 | C2 | semidirect |
| 5. #19151774 | C2 | semidirect |
| 6. #19151615 | C2 | semidirect |
| 7. #19151614 | C2 | semidirect |
| 8. #19151580 | C2 | semidirect |
| 9. C2×#137×C89 | C2 | semidirect |
| 23. #15668043 | C22 | semidirect |
| 26. C2×#13083558 | C22 | semidirect |
| 27. #15668010 | C22 | semidirect |
| 28. #15668001 | C22 | semidirect |
| 31. #15667971 | C22 | semidirect |
| 32. #15667939 | C22 | semidirect |
| 33. #15667938 | C22 | semidirect |
| 34. #15667930 | C22 | semidirect |
| 35. #15667928 | C22 | semidirect |
| 37. C22×Q8×C89 | C22 | semidirect |
| 39. #137×C89 | C22 | semidirect |
| 42. C2×M16×C89 | C22 | semidirect |
| 193. C89 | #3022 | semidirect |
| 196. C2×#137 | D89 | semidirect |
| 216. C22×Q8 | C2×D89 | semidirect |
| 220. #137 | C2×D89 | semidirect |
| 226. C2×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152434 | 2 |
| C2×#15668043 | 2 |
| #19152172 | 2 |
| #19151779 | 2 |
| #19151774 | 2 |
| #19151615 | 2 |
| #19151614 | 2 |
| #19151580 | 2 |
| C2×#137×C89 | 2 |
| #3022 | 89 |