Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
554 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21432073 | C2 | semidirect |
| 2. #21425184 | C2 | semidirect |
| 4. #21421921 | C2 | semidirect |
| 5. #21421919 | C2 | semidirect |
| 6. #21421916 | C2 | semidirect |
| 7. C59×#2041 | C2 | semidirect |
| 224. #2041 | D59 | semidirect |
| 258. C59 | #7746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432073 | 2 |
| #21425184 | 2 |
| #21425167 | 2 |
| #21421921 | 2 |
| #21421919 | 2 |
| #21421916 | 2 |
| C59×#2041 | 2 |
| #7746 | 59 |