Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15668001 | C2 | semidirect |
| 3. C2×#15667988 | C2 | semidirect |
| 4. #19151515 | C2 | semidirect |
| 5. #19151505 | C2 | semidirect |
| 6. #19151500 | C2 | semidirect |
| 7. #19151469 | C2 | semidirect |
| 8. C4×#13083551 | C2 | semidirect |
| 9. C2×C4⋊Q8×C89 | C2 | semidirect |
| 94. C2×C4×C89 | #41 | semidirect |
| 137. C89 | #2432 | semidirect |
| 139. C2×C4⋊Q8 | D89 | semidirect |
| 243. C2×C4 | #13083575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083575 | 2 |
| C2×#15668001 | 2 |
| C2×#15667988 | 2 |
| #19151515 | 2 |
| #19151505 | 2 |
| #19151500 | 2 |
| #19151469 | 2 |
| C4×#13083551 | 2 |
| C2×C4⋊Q8×C89 | 2 |
| #2432 | 89 |