Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21424928 | C2 | semidirect |
| 3. #21422819 | C2 | semidirect |
| 4. #21422818 | C2 | semidirect |
| 5. #21422730 | C2 | semidirect |
| 6. #21422603 | C2 | semidirect |
| 7. C59×#1505 | C2 | semidirect |
| 11. #16838117 | C4 | semidirect |
| 13. D4×D236 | C4 | semidirect |
| 20. #16837459 | C22 | semidirect |
| 21. #16837426 | C22 | semidirect |
| 30. C59×#432 | C22 | semidirect |
| 31. C59×#376 | C22 | semidirect |
| 233. #1505 | D59 | semidirect |
| 255. #432 | C2×D59 | semidirect |
| 258. #376 | C2×D59 | semidirect |
| 266. C59 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438501 | 2 |
| #21424928 | 2 |
| #21422819 | 2 |
| #21422818 | 2 |
| #21422730 | 2 |
| #21422603 | 2 |
| C59×#1505 | 2 |
| #8491 | 59 |