Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
514 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16837207 | C2 | semidirect |
| 4. C4×#14273661 | C2 | semidirect |
| 5. C2×C59×C4⋊C16 | C2 | semidirect |
| 11. #16837786 | C4 | semidirect |
| 133. C2×C4⋊C16 | D59 | semidirect |
| 157. C59 | #13254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837786 | 2 |
| C2×#16837207 | 2 |
| C2×#16837204 | 2 |
| C4×#14273661 | 2 |
| C2×C59×C4⋊C16 | 2 |
| #13254 | 59 |