Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21435101 | C2 | semidirect |
| 2. #21434471 | C2 | semidirect |
| 4. #21422809 | C2 | semidirect |
| 5. #21422693 | C2 | semidirect |
| 6. #21422607 | C2 | semidirect |
| 7. C59×#1300 | C2 | semidirect |
| 39. #14273727 | D4 | semidirect |
| 40. #14273727 | D4 | semidirect |
| 70. C4⋊C8×C59 | D4 | semidirect |
| 73. #97×C59 | D4 | semidirect |
| 201. #1300 | D59 | semidirect |
| 231. C59 | #10096 | semidirect |
| 265. C4⋊C8 | D236 | semidirect |
| 274. #97 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435101 | 2 |
| #21434471 | 2 |
| #21430202 | 2 |
| #21422809 | 2 |
| #21422693 | 2 |
| #21422607 | 2 |
| C59×#1300 | 2 |
| #10096 | 59 |