Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#19153040 | C2 | semidirect |
| 3. C2×#19153039 | C2 | semidirect |
| 4. #26038438 | C2 | semidirect |
| 5. #26038308 | C2 | semidirect |
| 6. #26038207 | C2 | semidirect |
| 7. #417×C179 | C2 | semidirect |
| 48. C4×Dic179 | D4 | semidirect |
| 128. C179 | #2039 | semidirect |
| 134. #417 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039017 | 2 |
| C2×#19153040 | 2 |
| C2×#19153039 | 2 |
| #26038438 | 2 |
| #26038308 | 2 |
| #26038207 | 2 |
| #417×C179 | 2 |
| #2039 | 179 |