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. #19153160 | C2 | semidirect |
| 2. #19153159 | C2 | semidirect |
| 3. #19153146 | C2 | semidirect |
| 4. #19153141 | C2 | semidirect |
| 5. #19153135 | C2 | semidirect |
| 6. C2×#15668248 | C2 | semidirect |
| 7. #131×C179 | C2 | semidirect |
| 10. #15668259 | C22 | semidirect |
| 12. C2×Dic358 | C22 | semidirect |
| 16. Dic716 | C22 | semidirect |
| 17. #15668248 | C22 | semidirect |
| 18. #15668248 | C22 | semidirect |
| 19. #15668248 | C22 | semidirect |
| 20. D1432 | C22 | semidirect |
| 22. M16×C179 | C22 | semidirect |
| 23. C2×C8×C179 | C22 | semidirect |
| 53. C179 | #577 | semidirect |
| 61. #131 | D179 | semidirect |
| 76. M16 | C2×D179 | semidirect |
| 77. C2×C8 | C2×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153160 | 2 |
| #19153159 | 2 |
| #19153146 | 2 |
| #19153141 | 2 |
| #19153135 | 2 |
| C2×#15668248 | 2 |
| #131×C179 | 2 |
| #577 | 179 |