Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #21426335 | C2 | semidirect |
| 3. #21426240 | C2 | semidirect |
| 4. #21422138 | C2 | semidirect |
| 5. #21422062 | C2 | semidirect |
| 6. #21422054 | C2 | semidirect |
| 7. C59×#1693 | C2 | semidirect |
| 17. C4⋊(C59⋊C16) | C22 | semidirect |
| 21. #16837178 | C22 | semidirect |
| 22. C59×#500 | C22 | semidirect |
| 25. C59×#334 | C22 | semidirect |
| 101. D472 | SD16 | semidirect |
| 164. #1693 | D59 | semidirect |
| 176. #500 | C2×D59 | semidirect |
| 191. #334 | C2×D59 | semidirect |
| 193. C59 | #12378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435708 | 2 |
| #21426335 | 2 |
| #21426240 | 2 |
| #21422138 | 2 |
| #21422062 | 2 |
| #21422054 | 2 |
| C59×#1693 | 2 |
| #12378 | 59 |