Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×#13083561 | C2 | semidirect |
| 3. C2×#15668001 | C2 | semidirect |
| 4. #19151983 | C2 | direct (N × H) |
| 5. C2×C8×Dic89 | C2 | semidirect |
| 6. C22×Q16×C89 | C2 | semidirect |
| 9. C2×#13083561 | C22 | semidirect |
| 14. #15668001 | C22 | semidirect |
| 17. C8×Dic89 | C22 | semidirect |
| 20. C2×Q16×C89 | C22 | semidirect |
| 75. C2×C89 | #495 | semidirect |
| 80. C89 | C2×#495 | semidirect |
| 81. C22×Q16 | D89 | semidirect |
| 90. C2×Q16 | C2×D89 | semidirect |
| 156. C2 | #19151983 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083561 | 2 |
| C22×D712 | 2 |
| C2×#15668001 | 2 |
| #19151983 | 2 |
| C2×C8×Dic89 | 2 |
| C22×Q16×C89 | 2 |
| C2×#495 | 89 |