Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 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 |
|---|---|---|
| 2. #21426458 | C2 | semidirect |
| 3. #21425016 | C2 | semidirect |
| 4. #21422538 | C2 | semidirect |
| 5. #21421989 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 7. C59×#1505 | C2 | semidirect |
| 11. #16837689 | C4 | semidirect |
| 12. #16837594 | C4 | semidirect |
| 46. C4⋊(C59⋊C8) | C2×C4 | semidirect |
| 57. C4⋊Q8×C59 | C2×C4 | semidirect |
| 58. #127×C59 | C2×C4 | semidirect |
| 158. D236 | #104 | semidirect |
| 193. #1505 | D59 | semidirect |
| 225. C59 | #9325 | semidirect |
| 232. C4⋊Q8 | C4×D59 | semidirect |
| 233. #127 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434183 | 2 |
| #21426458 | 2 |
| #21425016 | 2 |
| #21422538 | 2 |
| #21421989 | 2 |
| #21421951 | 2 |
| C59×#1505 | 2 |
| #9325 | 59 |