Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
372 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21422842 | C2 | semidirect |
| 3. C2×#16837152 | C2 | semidirect |
| 6. #21421947 | C2 | semidirect |
| 7. C59×#1283 | C2 | semidirect |
| 155. #1283 | D59 | semidirect |
| 181. C59 | #8607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432741 | 2 |
| #21422842 | 2 |
| C2×#16837152 | 2 |
| #21422484 | 2 |
| #21422481 | 2 |
| #21421947 | 2 |
| C59×#1283 | 2 |
| #8607 | 59 |