Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #19152396 | C2 | semidirect |
| 2. C2×#15668040 | C2 | semidirect |
| 3. #19152162 | C2 | semidirect |
| 4. #19151602 | C2 | semidirect |
| 5. #19151571 | C2 | semidirect |
| 6. #19151370 | C2 | semidirect |
| 7. #421×C89 | C2 | semidirect |
| 36. C2×Dic178 | D4 | semidirect |
| 43. C2×D356 | D4 | semidirect |
| 55. C2×#10623494 | D4 | semidirect |
| 70. M16×C89 | D4 | semidirect |
| 143. C89 | #2008 | semidirect |
| 147. #421 | D89 | semidirect |
| 208. M16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152396 | 2 |
| C2×#15668040 | 2 |
| #19152162 | 2 |
| #19151602 | 2 |
| #19151571 | 2 |
| #19151370 | 2 |
| #421×C89 | 2 |
| #2008 | 89 |