Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 278 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 |
|---|---|---|
| 4. C2×#19153031 | C2 | semidirect |
| 5. #26038344 | C2 | semidirect |
| 6. #26038198 | C2 | semidirect |
| 7. #428×C179 | C2 | semidirect |
| 120. C179 | #2038 | semidirect |
| 123. #428 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039015 | 2 |
| C2×#19153039 | 2 |
| #26038438 | 2 |
| C2×#19153031 | 2 |
| #26038344 | 2 |
| #26038198 | 2 |
| #428×C179 | 2 |
| #2038 | 179 |