Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
566 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 139 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. #21425852 | C2 | semidirect |
| 3. C2×#16837214 | C2 | semidirect |
| 4. C4×#108×C59 | C2 | semidirect |
| 35. #108×C59 | D4 | semidirect |
| 96. C4×C59 | #361 | semidirect |
| 103. C4×#108 | D59 | semidirect |
| 120. C59 | #13257 | semidirect |
| 139. #108 | D236 | semidirect |
| 199. C4 | #16837214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837779 | 2 |
| #21425852 | 2 |
| C2×#16837214 | 2 |
| C4×#108×C59 | 2 |
| #13257 | 59 |