Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21426911 | C2 | semidirect |
| 2. #21425016 | C2 | semidirect |
| 3. #21422694 | C2 | semidirect |
| 4. #21422643 | C2 | semidirect |
| 5. #21421962 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 25. C59×#496 | C4 | semidirect |
| 26. C59×#489 | C4 | semidirect |
| 60. C4⋊Q8×C59 | C2×C4 | semidirect |
| 61. #127×C59 | C2×C4 | semidirect |
| 78. #97×C59 | C2×C4 | semidirect |
| 231. #496 | Dic59 | semidirect |
| 232. #489 | Dic59 | semidirect |
| 252. C59 | #9381 | semidirect |
| 260. C4⋊Q8 | C2×Dic59 | semidirect |
| 261. #127 | C2×Dic59 | semidirect |
| 292. #97 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426911 | 2 |
| #21425016 | 2 |
| #21422694 | 2 |
| #21422643 | 2 |
| #21421962 | 2 |
| #21421951 | 2 |
| C59×#3213 | 2 |
| #9381 | 59 |