Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
576 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 576 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. #21427253 | C2 | semidirect |
| 2. #21424933 | C2 | semidirect |
| 3. #21422625 | C2 | semidirect |
| 4. #21422612 | C2 | semidirect |
| 5. #21422003 | C2 | semidirect |
| 6. #21421950 | C2 | semidirect |
| 26. C59×#481 | C4 | semidirect |
| 29. C59×#447 | C4 | semidirect |
| 57. C22×D4×C59 | C2×C4 | semidirect |
| 70. C2×C4⋊C4×C59 | C2×C4 | semidirect |
| 78. C22⋊C8×C59 | C2×C4 | semidirect |
| 259. #481 | Dic59 | semidirect |
| 262. #447 | Dic59 | semidirect |
| 279. C59 | #9343 | semidirect |
| 282. C22×D4 | C2×Dic59 | semidirect |
| 299. C2×C4⋊C4 | C2×Dic59 | semidirect |
| 320. C22⋊C8 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427253 | 2 |
| #21424933 | 2 |
| #21422625 | 2 |
| #21422612 | 2 |
| #21422003 | 2 |
| #21421950 | 2 |
| C59×#3192 | 2 |
| #9343 | 59 |