Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #21429458 | C2 | semidirect |
| 5. #21422526 | C2 | semidirect |
| 6. #21421955 | C2 | semidirect |
| 7. C59×#1479 | C2 | semidirect |
| 89. C2×Q8×C59 | SD16 | semidirect |
| 219. #1479 | D59 | semidirect |
| 252. C59 | #9999 | semidirect |
| 317. C2×Q8 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434128 | 2 |
| #21433568 | 2 |
| #21429458 | 2 |
| #21422657 | 2 |
| #21422526 | 2 |
| #21421955 | 2 |
| C59×#1479 | 2 |
| #9999 | 59 |