Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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×D16×D59 | C2 | semidirect |
| 2. #493×D59 | C2 | semidirect |
| 3. #21426346 | C2 | semidirect |
| 4. #21426345 | C2 | semidirect |
| 5. #21426344 | C2 | semidirect |
| 6. C4×C16×D59 | C2 | semidirect |
| 7. C59×#2246 | C2 | semidirect |
| 11. C2×D944 | C22 | semidirect |
| 12. C2×#14273668 | C22 | semidirect |
| 15. #16837779 | C22 | semidirect |
| 18. #16837777 | C22 | semidirect |
| 20. C4×C59⋊C16 | C22 | semidirect |
| 21. C16×Dic59 | C22 | semidirect |
| 22. C2×D16×C59 | C22 | semidirect |
| 23. C59×#493 | C22 | semidirect |
| 24. C4×C16×C59 | C22 | semidirect |
| 42. C16×D59 | D4 | semidirect |
| 79. C16×C59 | C2×D4 | semidirect |
| 80. C59⋊C16 | C2×D4 | semidirect |
| 98. C4×D59 | D16 | semidirect |
| 114. C4×C59 | C2×D16 | semidirect |
| 118. Dic59 | C2×D16 | semidirect |
| 124. #2246 | D59 | direct (N × H) |
| 130. D59 | #2246 | direct (N × H) |
| 137. C2×D16 | C2×D59 | semidirect |
| 143. #493 | C2×D59 | semidirect |
| 147. C4×C16 | C2×D59 | semidirect |
| 148. C59 | C2×#2246 | semidirect |
| 204. C16 | D4×D59 | semidirect |
| 239. C4 | D16×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D59 | 2 |
| #493×D59 | 2 |
| #21426346 | 2 |
| #21426345 | 2 |
| #21426344 | 2 |
| C4×C16×D59 | 2 |
| C59×#2246 | 2 |
| C2×#2246 | 59 |