Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26038716 | C2 | semidirect |
| 3. C8×D716 | C2 | semidirect |
| 4. #26038190 | C2 | semidirect |
| 5. #26038185 | C2 | semidirect |
| 6. #26038183 | C2 | semidirect |
| 7. #492×C179 | C2 | semidirect |
| 45. D716 | SD16 | semidirect |
| 65. C8×C179 | D8 | semidirect |
| 85. C179 | #1665 | semidirect |
| 87. #492 | D179 | semidirect |
| 151. C8 | #15668244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038716 | 2 |
| #26038631 | 2 |
| C8×D716 | 2 |
| #26038190 | 2 |
| #26038185 | 2 |
| #26038183 | 2 |
| #492×C179 | 2 |
| #1665 | 179 |