Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26038487 | C2 | semidirect |
| 2. #26038456 | C2 | semidirect |
| 3. #26038444 | C2 | semidirect |
| 4. #26038423 | C2 | semidirect |
| 5. C2×#19153030 | C2 | semidirect |
| 6. #26038211 | C2 | semidirect |
| 110. C179 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038487 | 2 |
| #26038456 | 2 |
| #26038444 | 2 |
| #26038423 | 2 |
| C2×#19153030 | 2 |
| #26038211 | 2 |
| C2×AGL(1,ℤ/8)×C179 | 2 |
| #2048 | 179 |