Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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×#16837241 | C2 | semidirect |
| 2. C2×#16837240 | C2 | semidirect |
| 3. C2×#16837237 | C2 | semidirect |
| 4. #21426354 | C2 | semidirect |
| 5. #21426344 | C2 | semidirect |
| 6. #21422229 | C2 | semidirect |
| 7. C2×C59×D32 | C2 | semidirect |
| 37. C59⋊C32 | D4 | semidirect |
| 45. C32×C59 | D4 | semidirect |
| 101. C2×D32 | D59 | semidirect |
| 125. C59 | #13729 | semidirect |
| 148. C32 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837241 | 2 |
| C2×#16837240 | 2 |
| C2×#16837237 | 2 |
| #21426354 | 2 |
| #21426344 | 2 |
| #21422229 | 2 |
| C2×C59×D32 | 2 |
| #13729 | 59 |