Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#16837836 | C2 | semidirect |
| 2. #21434523 | C2 | semidirect |
| 3. #493×D59 | C2 | semidirect |
| 4. #21426359 | C2 | semidirect |
| 5. #21426352 | C2 | semidirect |
| 6. #21426351 | C2 | semidirect |
| 7. #21426345 | C2 | semidirect |
| 8. C4×#14273666 | C2 | semidirect |
| 9. C59×#2246 | C2 | semidirect |
| 17. C2×#14273672 | C22 | semidirect |
| 18. C2×#14273671 | C22 | semidirect |
| 19. C2×#14273668 | C22 | semidirect |
| 22. #16837785 | C22 | semidirect |
| 23. #16837782 | C22 | semidirect |
| 30. #16837177 | C22 | semidirect |
| 31. C4×C59⋊C16 | C22 | semidirect |
| 32. C2×D16×C59 | C22 | semidirect |
| 34. C59×#493 | C22 | semidirect |
| 35. C4×C16×C59 | C22 | semidirect |
| 64. #14273666 | D4 | semidirect |
| 120. C16×C59 | C2×D4 | semidirect |
| 121. C59⋊C16 | C2×D4 | semidirect |
| 166. C4×C59 | #509 | semidirect |
| 179. #2246 | D59 | semidirect |
| 197. C2×D16 | C2×D59 | semidirect |
| 207. #493 | C2×D59 | semidirect |
| 212. C4×C16 | C2×D59 | semidirect |
| 213. C59 | #33717 | semidirect |
| 299. C16 | D4×D59 | semidirect |
| 346. C4 | #16837836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837836 | 2 |
| #21434523 | 2 |
| #493×D59 | 2 |
| #21426359 | 2 |
| #21426352 | 2 |
| #21426351 | 2 |
| #21426345 | 2 |
| C4×#14273666 | 2 |
| C59×#2246 | 2 |
| #33717 | 59 |