Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
460 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21425066 | C2 | semidirect |
| 3. #21424265 | C2 | semidirect |
| 4. C2×#16837144 | C2 | semidirect |
| 6. #21421977 | C2 | semidirect |
| 238. C59 | #10427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425066 | 2 |
| #21424913 | 2 |
| #21424265 | 2 |
| C2×#16837144 | 2 |
| C2×#16837142 | 2 |
| #21421977 | 2 |
| C59×#2820 | 2 |
| #10427 | 59 |