Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #21425073 | C2 | semidirect |
| 4. #21422784 | C2 | semidirect |
| 6. #21421971 | C2 | semidirect |
| 7. C59×#1831 | C2 | semidirect |
| 95. C42×C59 | SD16 | semidirect |
| 187. #1831 | D59 | semidirect |
| 218. C59 | #10521 | semidirect |
| 304. C42 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435413 | 2 |
| #21425073 | 2 |
| #21424924 | 2 |
| #21422784 | 2 |
| #21422771 | 2 |
| #21421971 | 2 |
| C59×#1831 | 2 |
| #10521 | 59 |