Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21435079 | C2 | semidirect |
| 2. #21434549 | C2 | semidirect |
| 3. #21430202 | C2 | semidirect |
| 4. #21422809 | C2 | semidirect |
| 5. #21422695 | C2 | semidirect |
| 6. #21421989 | C2 | semidirect |
| 7. C59×#1505 | C2 | semidirect |
| 56. C4⋊(C59⋊C8) | D4 | semidirect |
| 61. #14273638 | D4 | semidirect |
| 64. C4⋊Q8×C59 | D4 | semidirect |
| 65. #127×C59 | D4 | semidirect |
| 210. #1505 | D59 | semidirect |
| 242. C59 | #10088 | semidirect |
| 256. C4⋊Q8 | D236 | semidirect |
| 262. #127 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435079 | 2 |
| #21434549 | 2 |
| #21430202 | 2 |
| #21422809 | 2 |
| #21422695 | 2 |
| #21421989 | 2 |
| C59×#1505 | 2 |
| #10088 | 59 |