Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #21427206 | C2 | semidirect |
| 3. #21422719 | C2 | semidirect |
| 4. #21422605 | C2 | semidirect |
| 5. #21422603 | C2 | semidirect |
| 6. #21421990 | C2 | semidirect |
| 7. C59×#1300 | C2 | semidirect |
| 12. #16837796 | C4 | semidirect |
| 13. #16837791 | C4 | semidirect |
| 43. #14273727 | C2×C4 | semidirect |
| 44. #14273724 | C2×C4 | semidirect |
| 76. #97×C59 | C2×C4 | semidirect |
| 226. #1300 | D59 | semidirect |
| 257. C59 | #9441 | semidirect |
| 298. #97 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434562 | 2 |
| #21427206 | 2 |
| #21422719 | 2 |
| #21422605 | 2 |
| #21422603 | 2 |
| #21421990 | 2 |
| C59×#1300 | 2 |
| #9441 | 59 |