Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21437230 | C2 | semidirect |
| 2. #21433677 | C2 | semidirect |
| 3. #21425832 | C2 | semidirect |
| 4. #21425831 | C2 | semidirect |
| 5. #21425707 | C2 | semidirect |
| 6. #21422197 | C2 | semidirect |
| 7. C59×#3050 | C2 | semidirect |
| 38. C2×Dic236 | D4 | semidirect |
| 40. C2×D472 | D4 | semidirect |
| 56. C2×C59⋊C16 | D4 | semidirect |
| 58. #14273659 | D4 | semidirect |
| 67. C2×Q16×C59 | D4 | semidirect |
| 69. C2×D8×C59 | D4 | semidirect |
| 85. #106×C59 | D4 | semidirect |
| 228. #3050 | D59 | semidirect |
| 265. C59 | #13309 | semidirect |
| 278. C2×Q16 | C22⋊D59 | semidirect |
| 282. C2×D8 | C22⋊D59 | semidirect |
| 316. #106 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437230 | 2 |
| #21433677 | 2 |
| #21425832 | 2 |
| #21425831 | 2 |
| #21425707 | 2 |
| #21422197 | 2 |
| C59×#3050 | 2 |
| #13309 | 59 |