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. #21425816 | C2 | semidirect |
| 5. #21422202 | C2 | semidirect |
| 6. #21422201 | C2 | semidirect |
| 7. C59×#2141 | C2 | semidirect |
| 13. #16837657 | C4 | semidirect |
| 53. #14273659 | C2×C4 | semidirect |
| 62. C2×Q16×C59 | C2×C4 | semidirect |
| 176. #2141 | D59 | semidirect |
| 203. C59 | #13000 | semidirect |
| 211. C2×Q16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837657 | 2 |
| #21432684 | 2 |
| #21425816 | 2 |
| C2×#16837183 | 2 |
| #21422202 | 2 |
| #21422201 | 2 |
| C59×#2141 | 2 |
| #13000 | 59 |