Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
316 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 51 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. #19152223 | C2 | semidirect |
| 2. #19151749 | C2 | semidirect |
| 4. #19151336 | C2 | semidirect |
| 5. #19151335 | C2 | semidirect |
| 6. #19151321 | C2 | semidirect |
| 7. #450×C89 | C2 | semidirect |
| 29. C2×Dic178 | D4 | semidirect |
| 40. C4⋊Dic89 | D4 | semidirect |
| 51. C2×Q8×C89 | D4 | semidirect |
| 59. C4⋊C4×C89 | D4 | semidirect |
| 73. C22×D89 | SD16 | semidirect |
| 131. C89 | #1596 | semidirect |
| 134. #450 | D89 | semidirect |
| 162. C2×Q8 | C22⋊D89 | semidirect |
| 184. C4⋊C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152223 | 2 |
| #19151749 | 2 |
| #19151506 | 2 |
| #19151336 | 2 |
| #19151335 | 2 |
| #19151321 | 2 |
| #450×C89 | 2 |
| #1596 | 89 |