Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
458 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21426345 | C2 | semidirect |
| 2. #21426131 | C2 | semidirect |
| 3. #21423451 | C2 | semidirect |
| 4. #21422142 | C2 | semidirect |
| 5. #21422057 | C2 | semidirect |
| 6. D4⋊(C59⋊C16) | C2 | semidirect |
| 7. D4×D8×C59 | C2 | semidirect |
| 10. #16837779 | C22 | semidirect |
| 12. C4⋊(C59⋊C16) | C22 | semidirect |
| 14. C4×C59⋊C16 | C22 | semidirect |
| 15. #16837155 | C22 | semidirect |
| 78. D8×C59 | D8 | semidirect |
| 114. D4×C59 | D16 | semidirect |
| 156. D4×D8 | D59 | semidirect |
| 187. C59 | #12316 | semidirect |
| 245. D8 | #11745669 | semidirect |
| 282. D4 | #14273668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426345 | 2 |
| #21426131 | 2 |
| #21423451 | 2 |
| #21422142 | 2 |
| #21422057 | 2 |
| D4⋊(C59⋊C16) | 2 |
| D4×D8×C59 | 2 |
| #12316 | 59 |