Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
366 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 366 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. #21426333 | C2 | semidirect |
| 3. #21426234 | C2 | semidirect |
| 4. #21423619 | C2 | semidirect |
| 5. #21422140 | C2 | semidirect |
| 6. #21422064 | C2 | semidirect |
| 7. C59×#1330 | C2 | semidirect |
| 10. #16837807 | C22 | semidirect |
| 22. #16837153 | C22 | semidirect |
| 25. C59×C4⋊C16 | C22 | semidirect |
| 26. C59×#346 | C22 | semidirect |
| 165. #1330 | D59 | semidirect |
| 184. C4⋊C16 | C2×D59 | semidirect |
| 188. #346 | C2×D59 | semidirect |
| 191. C59 | #12376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435708 | 2 |
| #21426333 | 2 |
| #21426234 | 2 |
| #21423619 | 2 |
| #21422140 | 2 |
| #21422064 | 2 |
| C59×#1330 | 2 |
| #12376 | 59 |