Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21435011 | C2 | semidirect |
| 2. #21433556 | C2 | semidirect |
| 3. #21429038 | C2 | semidirect |
| 4. #21422763 | C2 | semidirect |
| 5. #21422488 | C2 | semidirect |
| 6. #21421999 | C2 | semidirect |
| 7. C59×#1502 | C2 | semidirect |
| 58. C4⋊(C59⋊C8) | D4 | semidirect |
| 59. C4⋊(C59⋊C8) | D4 | semidirect |
| 66. C4⋊Q8×C59 | D4 | semidirect |
| 67. #127×C59 | D4 | semidirect |
| 117. C2×D236 | D8 | semidirect |
| 237. #1502 | D59 | semidirect |
| 271. C59 | #10238 | semidirect |
| 285. C4⋊Q8 | D236 | semidirect |
| 292. #127 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435011 | 2 |
| #21433556 | 2 |
| #21429038 | 2 |
| #21422763 | 2 |
| #21422488 | 2 |
| #21421999 | 2 |
| C59×#1502 | 2 |
| #10238 | 59 |