Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21435079 | C2 | semidirect |
| 2. #21434564 | C2 | semidirect |
| 3. #21422565 | C2 | semidirect |
| 4. #21422513 | C2 | semidirect |
| 5. #21422449 | C2 | semidirect |
| 6. #21421969 | C2 | semidirect |
| 7. C59×#3214 | C2 | semidirect |
| 206. #3214 | D59 | semidirect |
| 245. C59 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435079 | 2 |
| #21434564 | 2 |
| #21422565 | 2 |
| #21422513 | 2 |
| #21422449 | 2 |
| #21421969 | 2 |
| C59×#3214 | 2 |
| #10120 | 59 |