Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #21425817 | C2 | semidirect |
| 4. #21425815 | C2 | semidirect |
| 6. #21422203 | C2 | semidirect |
| 7. C59×#1386 | C2 | semidirect |
| 14. #16837661 | C4 | semidirect |
| 33. C2×Dic236 | C2×C4 | semidirect |
| 69. #106×C59 | C2×C4 | semidirect |
| 179. #1386 | D59 | semidirect |
| 203. C59 | #13000 | semidirect |
| 246. #106 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837661 | 2 |
| #21432684 | 2 |
| #21425817 | 2 |
| #21425815 | 2 |
| C2×#16837183 | 2 |
| #21422203 | 2 |
| C59×#1386 | 2 |
| #13000 | 59 |