Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 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. C2×#16837449 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. C2×#16837214 | C2 | semidirect |
| 5. C2×#16837183 | C2 | semidirect |
| 6. #21422194 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 54. #14273663 | D4 | semidirect |
| 64. #108×C59 | D4 | semidirect |
| 179. #1383 | D59 | semidirect |
| 204. C59 | #13010 | semidirect |
| 242. #108 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837656 | 2 |
| C2×#16837449 | 2 |
| C2×#16837216 | 2 |
| C2×#16837214 | 2 |
| C2×#16837183 | 2 |
| #21422194 | 2 |
| C59×#1383 | 2 |
| #13010 | 59 |