Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 250 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 |
|---|---|---|
| 2. #26038787 | C2 | semidirect |
| 3. #26038716 | C2 | semidirect |
| 4. #26038182 | C2 | semidirect |
| 5. Q8⋊(C179⋊C8) | C2 | semidirect |
| 6. #26038166 | C2 | semidirect |
| 7. #462×C179 | C2 | semidirect |
| 99. C179 | #1641 | semidirect |
| 104. #462 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039111 | 2 |
| #26038787 | 2 |
| #26038716 | 2 |
| #26038182 | 2 |
| Q8⋊(C179⋊C8) | 2 |
| #26038166 | 2 |
| #462×C179 | 2 |
| #1641 | 179 |