Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
316 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 57 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. #19151748 | C2 | semidirect |
| 3. #19151335 | C2 | semidirect |
| 4. #19151322 | C2 | semidirect |
| 5. #543×C89 | C2 | semidirect |
| 31. C2×Q8×C89 | D4 | semidirect |
| 39. C4⋊C4×C89 | D4 | semidirect |
| 47. C23×C89 | SD16 | semidirect |
| 103. C89 | #1596 | semidirect |
| 104. #543 | D89 | semidirect |
| 125. C2×Q8 | C22⋊D89 | semidirect |
| 141. C4⋊C4 | C22⋊D89 | semidirect |
| 157. C23 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151748 | 2 |
| #19151507 | 2 |
| #19151335 | 2 |
| #19151322 | 2 |
| #543×C89 | 2 |
| #1596 | 89 |