Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26038811 | C2 | semidirect |
| 2. #26038734 | C2 | semidirect |
| 3. #26038729 | C2 | semidirect |
| 4. #26038183 | C2 | semidirect |
| 5. Q8⋊(C179⋊C8) | C2 | semidirect |
| 6. D4⋊(C179⋊C8) | C2 | semidirect |
| 58. Q8×C179 | SD16 | semidirect |
| 98. C179 | #1631 | semidirect |
| 153. Q8 | #15668247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038811 | 2 |
| #26038734 | 2 |
| #26038729 | 2 |
| #26038183 | 2 |
| Q8⋊(C179⋊C8) | 2 |
| D4⋊(C179⋊C8) | 2 |
| #550×C179 | 2 |
| #1631 | 179 |