Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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. #19151960 | C2 | direct (N × H) |
| 3. C2×#15667935 | C2 | semidirect |
| 5. C2×#15667923 | C2 | semidirect |
| 6. C2×C4⋊Q8×C89 | C2 | semidirect |
| 14. #15667935 | C22 | semidirect |
| 16. #15667923 | C22 | semidirect |
| 19. C4⋊Q8×C89 | C22 | semidirect |
| 82. C2×C89 | #489 | semidirect |
| 88. C89 | C2×#489 | semidirect |
| 89. C2×C4⋊Q8 | D89 | semidirect |
| 100. C4⋊Q8 | C2×D89 | semidirect |
| 171. C2 | #19151960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668000 | 2 |
| #19151960 | 2 |
| C2×#15667935 | 2 |
| C2×#15667932 | 2 |
| C2×#15667923 | 2 |
| C2×C4⋊Q8×C89 | 2 |
| C2×#489 | 89 |