Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 1. #26039154 | C2 | semidirect |
| 2. #26038812 | C2 | semidirect |
| 3. #26038635 | C2 | semidirect |
| 4. #26038634 | C2 | semidirect |
| 5. #26038187 | C2 | semidirect |
| 6. #26038168 | C2 | semidirect |
| 7. D4⋊C8×C179 | C2 | semidirect |
| 101. C179 | #1624 | semidirect |
| 109. 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 |
| #26038812 | 2 |
| #26038635 | 2 |
| #26038634 | 2 |
| #26038187 | 2 |
| #26038168 | 2 |
| D4⋊C8×C179 | 2 |
| #1624 | 179 |