Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
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. #21440006 | C2 | semidirect |
| 2. #21439991 | C2 | semidirect |
| 3. #21439985 | C2 | semidirect |
| 4. #21439980 | C2 | semidirect |
| 5. C2×#16838535 | C2 | semidirect |
| 6. #21439967 | C2 | semidirect |
| 7. 2−1+4×C239 | C2 | semidirect |
| 12. #16838538 | C22 | semidirect |
| 13. #16838536 | C22 | semidirect |
| 14. #16838535 | C22 | semidirect |
| 15. #16838535 | C22 | semidirect |
| 16. #16838533 | C22 | semidirect |
| 17. #16838532 | C22 | semidirect |
| 18. C2×C239⋊C8 | C22 | semidirect |
| 21. #41×C239 | C22 | semidirect |
| 23. C2×Q8×C239 | C22 | semidirect |
| 53. C239 | #577 | semidirect |
| 55. 2−1+4 | D239 | semidirect |
| 66. #41 | C2×D239 | semidirect |
| 68. C2×Q8 | C2×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440006 | 2 |
| #21439991 | 2 |
| #21439985 | 2 |
| #21439980 | 2 |
| C2×#16838535 | 2 |
| #21439967 | 2 |
| 2−1+4×C239 | 2 |
| #577 | 239 |