Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #19153159 | C2 | semidirect |
| 2. #19153144 | C2 | semidirect |
| 3. #19153138 | C2 | semidirect |
| 4. #19153133 | C2 | semidirect |
| 5. C2×#15668246 | C2 | semidirect |
| 6. #19153120 | C2 | semidirect |
| 7. 2−1+4×C179 | C2 | semidirect |
| 12. #15668249 | C22 | semidirect |
| 13. #15668247 | C22 | semidirect |
| 14. #15668246 | C22 | semidirect |
| 15. #15668246 | C22 | semidirect |
| 16. #15668244 | C22 | semidirect |
| 17. #15668243 | C22 | semidirect |
| 18. C2×C179⋊C8 | C22 | semidirect |
| 21. #41×C179 | C22 | semidirect |
| 23. C2×Q8×C179 | C22 | semidirect |
| 53. C179 | #577 | semidirect |
| 55. 2−1+4 | D179 | semidirect |
| 66. #41 | C2×D179 | semidirect |
| 68. C2×Q8 | C2×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153159 | 2 |
| #19153144 | 2 |
| #19153138 | 2 |
| #19153133 | 2 |
| C2×#15668246 | 2 |
| #19153120 | 2 |
| 2−1+4×C179 | 2 |
| #577 | 179 |