Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×C4⋊(C179⋊C8) | C2 | semidirect |
| 3. #26038171 | C2 | semidirect |
| 4. #26038168 | C2 | semidirect |
| 5. #431×C179 | C2 | semidirect |
| 24. #15668259 | C8 | semidirect |
| 53. Dic358 | C2×C8 | semidirect |
| 55. D716 | C2×C8 | semidirect |
| 101. C179 | #1477 | semidirect |
| 104. #431 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668259 | 2 |
| C2×C4⋊(C179⋊C8) | 2 |
| #26038171 | 2 |
| #26038168 | 2 |
| #431×C179 | 2 |
| #1477 | 179 |