Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16837845 | C2 | semidirect |
| 3. #21433752 | C2 | semidirect |
| 4. C2×#16837217 | C2 | semidirect |
| 5. #21425831 | C2 | semidirect |
| 6. #21425725 | C2 | semidirect |
| 7. C59×#1389 | C2 | semidirect |
| 206. #1389 | D59 | semidirect |
| 236. C59 | #13311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837845 | 2 |
| #21433817 | 2 |
| #21433752 | 2 |
| C2×#16837217 | 2 |
| #21425831 | 2 |
| #21425725 | 2 |
| C59×#1389 | 2 |
| #13311 | 59 |