Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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. #19152071 | C2 | semidirect |
| 3. C2×#15667926 | C2 | semidirect |
| 4. #19151454 | C2 | semidirect |
| 5. #19151365 | C2 | semidirect |
| 6. #19151364 | C2 | semidirect |
| 7. #379×C89 | C2 | semidirect |
| 11. #15667981 | C4 | semidirect |
| 38. C22×Dic89 | D4 | semidirect |
| 48. C22⋊Dic89 | C2×C4 | semidirect |
| 58. C24×C89 | C2×C4 | semidirect |
| 61. C22×C4×C89 | D4 | semidirect |
| 95. C22×D89 | C22⋊C4 | semidirect |
| 113. C2×Dic89 | C22⋊C4 | semidirect |
| 161. C89 | #1889 | semidirect |
| 166. #379 | D89 | semidirect |
| 195. C24 | C4×D89 | semidirect |
| 211. C22×C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667981 | 2 |
| #19152071 | 2 |
| C2×#15667926 | 2 |
| #19151454 | 2 |
| #19151365 | 2 |
| #19151364 | 2 |
| #379×C89 | 2 |
| #1889 | 89 |