Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21426821 | C2 | semidirect |
| 3. #21424928 | C2 | semidirect |
| 4. #21422763 | C2 | semidirect |
| 5. #21422657 | C2 | semidirect |
| 6. #21421955 | C2 | semidirect |
| 7. C59×#1274 | C2 | semidirect |
| 11. #16837779 | C4 | semidirect |
| 12. #16837749 | C4 | semidirect |
| 34. #14273727 | C2×C4 | semidirect |
| 38. #14273724 | C2×C4 | semidirect |
| 66. C4×C8×C59 | C2×C4 | semidirect |
| 106. C42×C59 | D8 | semidirect |
| 211. #1274 | D59 | semidirect |
| 238. C59 | #9299 | semidirect |
| 276. C4×C8 | C4×D59 | semidirect |
| 331. C42 | D472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435016 | 2 |
| #21426821 | 2 |
| #21424928 | 2 |
| #21422763 | 2 |
| #21422657 | 2 |
| #21421955 | 2 |
| C59×#1274 | 2 |
| #9299 | 59 |