Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 414 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. #21422690 | C2 | semidirect |
| 4. #21422518 | C2 | semidirect |
| 6. #21422385 | C2 | semidirect |
| 7. C4×#108×C59 | C2 | semidirect |
| 172. C4×#108 | D59 | semidirect |
| 206. C59 | #9728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434655 | 2 |
| #21422690 | 2 |
| #21422687 | 2 |
| #21422518 | 2 |
| #21422514 | 2 |
| #21422385 | 2 |
| C4×#108×C59 | 2 |
| #9728 | 59 |