Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
622 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 622 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. #21435011 | C2 | semidirect |
| 2. C2×#16837792 | C2 | semidirect |
| 3. #21422809 | C2 | semidirect |
| 4. #21422707 | C2 | semidirect |
| 5. #21422448 | C2 | semidirect |
| 6. #21421994 | C2 | semidirect |
| 7. C59×#3213 | C2 | semidirect |
| 195. #3213 | D59 | semidirect |
| 232. C59 | #10128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435011 | 2 |
| C2×#16837792 | 2 |
| #21422809 | 2 |
| #21422707 | 2 |
| #21422448 | 2 |
| #21421994 | 2 |
| C59×#3213 | 2 |
| #10128 | 59 |