Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
518 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#16837687 | C2 | semidirect |
| 4. #21422776 | C2 | semidirect |
| 6. #21421992 | C2 | semidirect |
| 7. C59×#1461 | C2 | semidirect |
| 198. #1461 | D59 | semidirect |
| 229. C59 | #10189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435226 | 2 |
| C2×#16837687 | 2 |
| #21433568 | 2 |
| #21422776 | 2 |
| #21422496 | 2 |
| #21421992 | 2 |
| C59×#1461 | 2 |
| #10189 | 59 |