Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26038819 | C2 | semidirect |
| 3. #26038730 | C2 | semidirect |
| 4. #26038729 | C2 | semidirect |
| 5. #26038187 | C2 | semidirect |
| 6. #26038168 | C2 | semidirect |
| 7. D4⋊C8×C179 | C2 | semidirect |
| 92. C179 | #1634 | semidirect |
| 100. D4⋊C8 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039154 | 2 |
| #26038819 | 2 |
| #26038730 | 2 |
| #26038729 | 2 |
| #26038187 | 2 |
| #26038168 | 2 |
| D4⋊C8×C179 | 2 |
| #1634 | 179 |