Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 498 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. #21432947 | C2 | semidirect |
| 3. #21425831 | C2 | semidirect |
| 4. #21425811 | C2 | semidirect |
| 5. #21424992 | C2 | semidirect |
| 6. #21422181 | C2 | semidirect |
| 7. C59×#1384 | C2 | semidirect |
| 13. C2×#14273672 | C4 | semidirect |
| 14. C2×D944 | C4 | semidirect |
| 33. C2×Dic236 | C2×C4 | semidirect |
| 39. C2×D472 | C2×C4 | semidirect |
| 62. C2×C16×C59 | C2×C4 | semidirect |
| 173. #1384 | D59 | semidirect |
| 200. C59 | #13033 | semidirect |
| 231. C2×C16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837840 | 2 |
| #21432947 | 2 |
| #21425831 | 2 |
| #21425811 | 2 |
| #21424992 | 2 |
| #21422181 | 2 |
| C59×#1384 | 2 |
| #13033 | 59 |