Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
774 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21426937 | C2 | semidirect |
| 2. #21424933 | C2 | semidirect |
| 3. #21424040 | C2 | semidirect |
| 4. #21422612 | C2 | semidirect |
| 5. #21422001 | C2 | semidirect |
| 6. #21421981 | C2 | semidirect |
| 22. C2×AGL(1,ℤ/8)×C59 | C4 | semidirect |
| 27. C59×#417 | C4 | semidirect |
| 155. Q8×C59 | #99 | semidirect |
| 246. C2×AGL(1,ℤ/8) | Dic59 | semidirect |
| 253. #417 | Dic59 | semidirect |
| 266. C59 | #9368 | semidirect |
| 393. Q8 | #14273642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426937 | 2 |
| #21424933 | 2 |
| #21424040 | 2 |
| #21422612 | 2 |
| #21422001 | 2 |
| #21421981 | 2 |
| C59×#3006 | 2 |
| #9368 | 59 |