Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
954 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21435479 | C2 | semidirect |
| 3. #21423236 | C2 | semidirect |
| 4. #21423217 | C2 | semidirect |
| 5. #21423174 | C2 | semidirect |
| 6. #21423155 | C2 | semidirect |
| 7. #21422831 | C2 | semidirect |
| 8. #21422551 | C2 | semidirect |
| 9. C59×#3550 | C2 | semidirect |
| 186. #3550 | D59 | semidirect |
| 227. C59 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435479 | 2 |
| #21434522 | 2 |
| #21423236 | 2 |
| #21423217 | 2 |
| #21423174 | 2 |
| #21423155 | 2 |
| #21422831 | 2 |
| #21422551 | 2 |
| C59×#3550 | 2 |
| #18688 | 59 |