Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21437232 | C2 | semidirect |
| 2. #21433817 | C2 | semidirect |
| 3. #21433759 | C2 | semidirect |
| 4. C2×#16837211 | C2 | semidirect |
| 5. #21425823 | C2 | semidirect |
| 6. #21425723 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 50. C2×Dic236 | D4 | semidirect |
| 54. C2×D472 | D4 | semidirect |
| 83. C2×C16×C59 | D4 | semidirect |
| 85. #108×C59 | D4 | semidirect |
| 226. #1383 | D59 | semidirect |
| 259. C59 | #13318 | semidirect |
| 306. C2×C16 | D236 | semidirect |
| 308. #108 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437232 | 2 |
| #21433817 | 2 |
| #21433759 | 2 |
| C2×#16837211 | 2 |
| #21425823 | 2 |
| #21425723 | 2 |
| C59×#1383 | 2 |
| #13318 | 59 |