Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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. C2×#19150220 | C2 | semidirect |
| 2. C2×#19150216 | C2 | semidirect |
| 3. #26013615 | C2 | semidirect |
| 5. #26013572 | C2 | semidirect |
| 6. #26013561 | C2 | semidirect |
| 7. #103×C349 | C2 | semidirect |
| 30. #14584095 | D4 | semidirect |
| 55. C349 | #468 | semidirect |
| 62. #103 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150220 | 2 |
| C2×#19150216 | 2 |
| #26013615 | 2 |
| #26013614 | 2 |
| #26013572 | 2 |
| #26013561 | 2 |
| #103×C349 | 2 |
| #468 | 349 |