Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1280 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1280 conjugacy classes of subgroups — too many to draw. Only its 191 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. C2×#16838006 | C2 | semidirect |
| 2. C2×#16837778 | C2 | semidirect |
| 3. C2×#16837767 | C2 | semidirect |
| 4. #21429849 | C2 | semidirect |
| 5. #21425093 | C2 | semidirect |
| 6. #21425060 | C2 | semidirect |
| 7. #21424442 | C2 | semidirect |
| 8. #21423865 | C2 | semidirect |
| 9. C59×#1961 | C2 | semidirect |
| 48. #14273719 | D4 | semidirect |
| 74. #127×C59 | D4 | semidirect |
| 207. #1961 | D59 | semidirect |
| 242. C59 | #25608 | semidirect |
| 259. #127 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838006 | 2 |
| C2×#16837778 | 2 |
| C2×#16837767 | 2 |
| #21429849 | 2 |
| #21425093 | 2 |
| #21425060 | 2 |
| #21424442 | 2 |
| #21423865 | 2 |
| C59×#1961 | 2 |
| #25608 | 59 |