Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
772 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 117 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×#16837715 | C2 | semidirect |
| 3. C2×#16837137 | C2 | semidirect |
| 4. C2×#16837136 | C2 | semidirect |
| 5. #21422364 | C2 | semidirect |
| 6. #21421938 | C2 | semidirect |
| 7. C2×C59×#480 | C2 | semidirect |
| 51. C22⋊(C59⋊C8) | D4 | semidirect |
| 72. C2×C4⋊C4×C59 | D4 | semidirect |
| 77. C22⋊C8×C59 | D4 | semidirect |
| 238. C2×#480 | D59 | semidirect |
| 277. C59 | #9970 | semidirect |
| 307. C2×C4⋊C4 | C22⋊D59 | semidirect |
| 319. C22⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837715 | 2 |
| #21430200 | 2 |
| C2×#16837137 | 2 |
| C2×#16837136 | 2 |
| #21422364 | 2 |
| #21421938 | 2 |
| C2×C59×#480 | 2 |
| #9970 | 59 |