Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26038465 | C2 | semidirect |
| 3. #26038436 | C2 | semidirect |
| 4. #26038413 | C2 | semidirect |
| 5. #26038412 | C2 | semidirect |
| 6. #26038195 | C2 | semidirect |
| 7. #416×C179 | C2 | semidirect |
| 118. C179 | #2053 | semidirect |
| 123. #416 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039237 | 2 |
| #26038465 | 2 |
| #26038436 | 2 |
| #26038413 | 2 |
| #26038412 | 2 |
| #26038195 | 2 |
| #416×C179 | 2 |
| #2053 | 179 |