Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #26038202 | C2 | semidirect |
| 5. #26038201 | C2 | semidirect |
| 6. #26038201 | C2 | semidirect |
| 7. C2×#106×C179 | C2 | semidirect |
| 116. C179 | #2077 | semidirect |
| 118. C2×#106 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×D179)⋊C8 | 2 |
| #26038296 | 2 |
| #26038202 | 2 |
| #26038201 | 2 |
| C2×#106×C179 | 2 |
| #2077 | 179 |