Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21427206 | C2 | semidirect |
| 3. #21422719 | C2 | semidirect |
| 4. #21422604 | C2 | semidirect |
| 5. #21421989 | C2 | semidirect |
| 6. #21421988 | C2 | semidirect |
| 7. C59×#1505 | C2 | semidirect |
| 11. #16837794 | C4 | semidirect |
| 12. #16837789 | C4 | semidirect |
| 58. #14273638 | C2×C4 | semidirect |
| 66. C4⋊Q8×C59 | C2×C4 | semidirect |
| 67. #127×C59 | C2×C4 | semidirect |
| 224. #1505 | D59 | semidirect |
| 257. C59 | #9441 | semidirect |
| 271. C4⋊Q8 | C4×D59 | semidirect |
| 272. #127 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434564 | 2 |
| #21427206 | 2 |
| #21422719 | 2 |
| #21422604 | 2 |
| #21421989 | 2 |
| #21421988 | 2 |
| C59×#1505 | 2 |
| #9441 | 59 |