Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
346 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21436444 | C2 | semidirect |
| 2. #21426319 | C2 | semidirect |
| 3. #21426128 | C2 | semidirect |
| 4. #21422152 | C2 | semidirect |
| 5. #21422056 | C2 | semidirect |
| 6. D4⋊(C59⋊C16) | C2 | semidirect |
| 7. C59×#1667 | C2 | semidirect |
| 97. D4×C59 | D16 | semidirect |
| 141. #1667 | D59 | semidirect |
| 168. C59 | #12340 | semidirect |
| 246. D4 | #14273668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436444 | 2 |
| #21426319 | 2 |
| #21426128 | 2 |
| #21422152 | 2 |
| #21422056 | 2 |
| D4⋊(C59⋊C16) | 2 |
| C59×#1667 | 2 |
| #12340 | 59 |