Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21429458 | C2 | semidirect |
| 4. #21422524 | C2 | semidirect |
| 5. #21422491 | C2 | semidirect |
| 6. #21421956 | C2 | semidirect |
| 94. C2×Q8×C59 | SD16 | semidirect |
| 252. C59 | #9999 | semidirect |
| 317. C2×Q8 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434123 | 2 |
| #21429458 | 2 |
| #21422656 | 2 |
| #21422524 | 2 |
| #21422491 | 2 |
| #21421956 | 2 |
| C59×#3037 | 2 |
| #9999 | 59 |