Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
520 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21437230 | C2 | semidirect |
| 2. #21433816 | C2 | semidirect |
| 3. C2×#16837209 | C2 | semidirect |
| 4. C2×#16837208 | C2 | semidirect |
| 5. #21425710 | C2 | semidirect |
| 6. #21422199 | C2 | semidirect |
| 7. C59×#3067 | C2 | semidirect |
| 218. #3067 | D59 | semidirect |
| 255. C59 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437230 | 2 |
| #21433816 | 2 |
| C2×#16837209 | 2 |
| C2×#16837208 | 2 |
| #21425710 | 2 |
| #21422199 | 2 |
| C59×#3067 | 2 |
| #13312 | 59 |