Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21434834 | C2 | semidirect |
| 2. #21426310 | C2 | semidirect |
| 3. #21426267 | C2 | semidirect |
| 4. #21426172 | C2 | semidirect |
| 5. #21426042 | C2 | semidirect |
| 6. #21425994 | C2 | semidirect |
| 7. #21425908 | C2 | semidirect |
| 8. C59×#2956 | C2 | semidirect |
| 11. #16837800 | C22 | semidirect |
| 12. #16837779 | C22 | semidirect |
| 17. #16837515 | C22 | semidirect |
| 18. #16837226 | C22 | semidirect |
| 19. #16837223 | C22 | semidirect |
| 20. #16837214 | C22 | semidirect |
| 23. #16837180 | C22 | semidirect |
| 89. Q16×C59 | #41 | semidirect |
| 93. D8×C59 | #41 | semidirect |
| 166. #2956 | D59 | semidirect |
| 202. C59 | #33688 | semidirect |
| 259. Q16 | #11745685 | semidirect |
| 265. D8 | #11745685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434834 | 2 |
| #21426310 | 2 |
| #21426267 | 2 |
| #21426172 | 2 |
| #21426042 | 2 |
| #21425994 | 2 |
| #21425908 | 2 |
| C59×#2956 | 2 |
| #33688 | 59 |