Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
374 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15667936 | C2 | semidirect |
| 5. #19151360 | C2 | semidirect |
| 6. #19151353 | C2 | semidirect |
| 7. C2×C4×Q8×C89 | C2 | semidirect |
| 11. C2×#13083561 | C4 | semidirect |
| 73. Q8×C89 | C22⋊C4 | semidirect |
| 85. C2×C4×C89 | SD16 | semidirect |
| 133. C89 | #1880 | semidirect |
| 135. C2×C4×Q8 | D89 | semidirect |
| 206. Q8 | #13083551 | semidirect |
| 225. C2×C4 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083561 | 2 |
| C2×#15667936 | 2 |
| C2×#15667932 | 2 |
| #19151500 | 2 |
| #19151360 | 2 |
| #19151353 | 2 |
| C2×C4×Q8×C89 | 2 |
| #1880 | 89 |