Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26039067 | C2 | semidirect |
| 4. #26038207 | C2 | semidirect |
| 5. #26038200 | C2 | semidirect |
| 6. #26038198 | C2 | semidirect |
| 49. C2×D4×C179 | Q8 | semidirect |
| 112. C179 | #2027 | semidirect |
| 145. C2×D4 | Dic358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039067 | 2 |
| #26038444 | 2 |
| #26038342 | 2 |
| #26038207 | 2 |
| #26038200 | 2 |
| #26038198 | 2 |
| #418×C179 | 2 |
| #2027 | 179 |