Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
604 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21425330 | C2 | semidirect |
| 2. #21425183 | C2 | semidirect |
| 4. #21421922 | C2 | semidirect |
| 5. #21421919 | C2 | semidirect |
| 6. #21421917 | C2 | semidirect |
| 7. C59×#2732 | C2 | semidirect |
| 72. C2×Q8×C59 | D8 | semidirect |
| 76. C2×D4×C59 | SD16 | semidirect |
| 230. #2732 | D59 | semidirect |
| 265. C59 | #7735 | semidirect |
| 311. C2×Q8 | #11745669 | semidirect |
| 333. C2×D4 | #11745671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425330 | 2 |
| #21425183 | 2 |
| #21425166 | 2 |
| #21421922 | 2 |
| #21421919 | 2 |
| #21421917 | 2 |
| C59×#2732 | 2 |
| #7735 | 59 |