Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26039205 | C2 | semidirect |
| 3. #26038444 | C2 | semidirect |
| 4. #26038412 | C2 | semidirect |
| 5. #26038196 | C2 | semidirect |
| 6. #26038195 | C2 | semidirect |
| 7. #418×C179 | C2 | semidirect |
| 13. #19153109 | C4 | semidirect |
| 14. #19153100 | C4 | semidirect |
| 37. C2×C179⋊C8 | D4 | semidirect |
| 56. C2×C8×C179 | D4 | semidirect |
| 115. C179 | #1910 | semidirect |
| 120. #418 | D179 | semidirect |
| 165. C2×C8 | C22⋊D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039205 | 2 |
| #26039006 | 2 |
| #26038444 | 2 |
| #26038412 | 2 |
| #26038196 | 2 |
| #26038195 | 2 |
| #418×C179 | 2 |
| #1910 | 179 |