Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
316 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19153046 | C2 | semidirect |
| 3. C2×#19153044 | C2 | semidirect |
| 5. #26038201 | C2 | semidirect |
| 6. #26038201 | C2 | semidirect |
| 18. C22⋊(C179⋊C8) | C4 | semidirect |
| 120. C179 | #1854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153072 | 2 |
| C2×#19153046 | 2 |
| C2×#19153044 | 2 |
| C2×C22⋊(C179⋊C8) | 2 |
| #26038201 | 2 |
| #380×C179 | 2 |
| #1854 | 179 |