Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
604 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16837840 | C2 | semidirect |
| 2. #21433705 | C2 | semidirect |
| 3. C2×#16837655 | C2 | semidirect |
| 4. C2×#16837213 | C2 | semidirect |
| 5. #21425813 | C2 | semidirect |
| 6. #21422202 | C2 | semidirect |
| 7. C2×C59×#349 | C2 | semidirect |
| 38. C2×Dic236 | D4 | semidirect |
| 45. C2×D472 | D4 | semidirect |
| 46. C2×D472 | D4 | semidirect |
| 59. #14273661 | D4 | semidirect |
| 62. #14273659 | D4 | semidirect |
| 78. M32×C59 | D4 | semidirect |
| 219. C2×#349 | D59 | semidirect |
| 251. C59 | #13316 | semidirect |
| 292. M32 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837840 | 2 |
| #21433705 | 2 |
| C2×#16837655 | 2 |
| C2×#16837213 | 2 |
| #21425813 | 2 |
| #21422202 | 2 |
| C2×C59×#349 | 2 |
| #13316 | 59 |