Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
550 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21435221 | C2 | semidirect |
| 2. C2×#16837683 | C2 | semidirect |
| 4. #21422776 | C2 | semidirect |
| 5. #21422416 | C2 | semidirect |
| 6. #21421993 | C2 | semidirect |
| 7. C59×#1480 | C2 | semidirect |
| 206. #1480 | D59 | semidirect |
| 239. C59 | #10188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435221 | 2 |
| C2×#16837683 | 2 |
| #21433556 | 2 |
| #21422776 | 2 |
| #21422416 | 2 |
| #21421993 | 2 |
| C59×#1480 | 2 |
| #10188 | 59 |