Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26038844 | C2 | semidirect |
| 4. #26038649 | C2 | semidirect |
| 5. #26038184 | C2 | semidirect |
| 7. Q8⋊C8×C179 | C2 | semidirect |
| 57. D716 | Q16 | semidirect |
| 92. C179 | #1649 | semidirect |
| 99. Q8⋊C8 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D716 | 2 |
| #26038844 | 2 |
| #26038720 | 2 |
| #26038649 | 2 |
| #26038184 | 2 |
| #26038168 | 2 |
| Q8⋊C8×C179 | 2 |
| #1649 | 179 |