Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21432684 | C2 | semidirect |
| 3. #21425813 | C2 | semidirect |
| 4. #21425811 | C2 | semidirect |
| 5. C2×#16837183 | C2 | semidirect |
| 6. #21422203 | C2 | semidirect |
| 7. C59×#1386 | C2 | semidirect |
| 14. #16837656 | C4 | semidirect |
| 34. C2×D472 | C2×C4 | semidirect |
| 55. #14273661 | D4 | semidirect |
| 66. #107×C59 | D4 | semidirect |
| 69. #106×C59 | C2×C4 | semidirect |
| 187. #1386 | D59 | semidirect |
| 212. C59 | #12999 | semidirect |
| 250. #107 | D236 | semidirect |
| 255. #106 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837656 | 2 |
| #21432684 | 2 |
| #21425813 | 2 |
| #21425811 | 2 |
| C2×#16837183 | 2 |
| #21422203 | 2 |
| C59×#1386 | 2 |
| #12999 | 59 |