Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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. #364×D59 | C2 | semidirect |
| 3. #21422381 | C2 | semidirect |
| 4. #21422073 | C2 | semidirect |
| 5. #21422072 | C2 | semidirect |
| 6. #21422071 | C2 | semidirect |
| 7. C59×#1336 | C2 | semidirect |
| 20. #16837223 | C22 | semidirect |
| 22. #16837123 | C22 | semidirect |
| 25. C59×#364 | C22 | semidirect |
| 26. C59×#322 | C22 | semidirect |
| 28. #14273750 | C8 | semidirect |
| 32. #14273746 | C8 | semidirect |
| 33. Q16×D59 | C8 | semidirect |
| 35. D8×D59 | C8 | semidirect |
| 181. #1336 | D59 | semidirect |
| 203. #364 | C2×D59 | semidirect |
| 205. #322 | C2×D59 | semidirect |
| 207. C59 | #11604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #443×D59 | 2 |
| #364×D59 | 2 |
| #21422381 | 2 |
| #21422073 | 2 |
| #21422072 | 2 |
| #21422071 | 2 |
| C59×#1336 | 2 |
| #11604 | 59 |