Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 4. #26038200 | C2 | semidirect |
| 5. #26038199 | C2 | semidirect |
| 6. #26038198 | C2 | semidirect |
| 7. #339×C179 | C2 | semidirect |
| 12. M16×D179 | C4 | semidirect |
| 15. #19153071 | C4 | semidirect |
| 18. #19153070 | C4 | semidirect |
| 21. C4⋊C4×D179 | C4 | semidirect |
| 42. #15668243 | C2×C4 | semidirect |
| 55. C4×Dic179 | C2×C4 | semidirect |
| 59. M16×C179 | C2×C4 | semidirect |
| 65. C42×C179 | C2×C4 | semidirect |
| 125. C179 | #1733 | semidirect |
| 133. #339 | D179 | semidirect |
| 173. M16 | C4×D179 | semidirect |
| 191. C42 | C4×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D179 | 2 |
| C2×#19153070 | 2 |
| #117×D179 | 2 |
| #26038200 | 2 |
| #26038199 | 2 |
| #26038198 | 2 |
| #339×C179 | 2 |
| #1733 | 179 |