Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 2. C2×#15667938 | C2 | semidirect |
| 3. #19151597 | C2 | semidirect |
| 4. C2×#15667928 | C2 | semidirect |
| 5. #19151499 | C2 | semidirect |
| 6. #19151357 | C2 | semidirect |
| 7. #428×C89 | C2 | semidirect |
| 56. M16×C89 | D4 | semidirect |
| 131. C89 | #2037 | semidirect |
| 133. #428 | D89 | semidirect |
| 181. M16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152167 | 2 |
| C2×#15667938 | 2 |
| #19151597 | 2 |
| C2×#15667928 | 2 |
| #19151499 | 2 |
| #19151357 | 2 |
| #428×C89 | 2 |
| #2037 | 89 |