Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
768 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. #21422217 | C2 | semidirect |
| 4. #21422216 | C2 | semidirect |
| 5. C59×#1391 | C2 | semidirect |
| 7. C22×#11745659 | C4 | semidirect |
| 8. C2×M16×D59 | C4 | semidirect |
| 13. #16837374 | C4 | semidirect |
| 15. #99×D59 | C4 | semidirect |
| 16. #16837370 | C4 | semidirect |
| 18. #16837368 | C4 | semidirect |
| 35. C2×#11745664 | C2×C4 | semidirect |
| 41. C22×C59⋊C8 | C2×C4 | semidirect |
| 51. #14273642 | C2×C4 | semidirect |
| 58. C2×M16×C59 | C2×C4 | semidirect |
| 59. C22×C8×C59 | C2×C4 | semidirect |
| 62. #99×C59 | C2×C4 | semidirect |
| 209. #1391 | D59 | semidirect |
| 234. C59 | #12577 | semidirect |
| 254. C2×M16 | C4×D59 | semidirect |
| 257. C22×C8 | C4×D59 | semidirect |
| 271. #99 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #410×D59 | 2 |
| #21432538 | 2 |
| #21422217 | 2 |
| #21422216 | 2 |
| C59×#1391 | 2 |
| #12577 | 59 |