Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16837449 | C2 | semidirect |
| 3. #21425824 | C2 | semidirect |
| 4. C2×#16837183 | C2 | semidirect |
| 5. #21422211 | C2 | semidirect |
| 6. #21422210 | C2 | semidirect |
| 7. C59×#2143 | C2 | semidirect |
| 50. #14273663 | D4 | semidirect |
| 70. #108×C59 | D4 | semidirect |
| 182. #2143 | D59 | semidirect |
| 211. C59 | #12998 | semidirect |
| 251. #108 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433701 | 2 |
| C2×#16837449 | 2 |
| #21425824 | 2 |
| C2×#16837183 | 2 |
| #21422211 | 2 |
| #21422210 | 2 |
| C59×#2143 | 2 |
| #12998 | 59 |