Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 254 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. #26038487 | C2 | semidirect |
| 5. C2×#19153032 | C2 | semidirect |
| 6. #26038209 | C2 | semidirect |
| 7. #419×C179 | C2 | semidirect |
| 105. C179 | #2049 | semidirect |
| 110. #419 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153144 | 2 |
| #26038487 | 2 |
| #26038457 | 2 |
| #26038421 | 2 |
| C2×#19153032 | 2 |
| #26038209 | 2 |
| #419×C179 | 2 |
| #2049 | 179 |