Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26038786 | C2 | semidirect |
| 3. #26038724 | C2 | semidirect |
| 4. #26038645 | C2 | semidirect |
| 5. #26038182 | C2 | semidirect |
| 6. #26038168 | C2 | semidirect |
| 7. Q8⋊C8×C179 | C2 | semidirect |
| 70. Q8×C179 | SD16 | semidirect |
| 99. C179 | #1642 | semidirect |
| 106. Q8⋊C8 | D179 | semidirect |
| 155. Q8 | #15668248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039111 | 2 |
| #26038786 | 2 |
| #26038724 | 2 |
| #26038645 | 2 |
| #26038182 | 2 |
| #26038168 | 2 |
| Q8⋊C8×C179 | 2 |
| #1642 | 179 |