Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
588 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21421922 | C2 | semidirect |
| 3. C59×#2811 | C2 | semidirect |
| 31. C2×Q8×C59 | SD16 | semidirect |
| 81. #2811 | D59 | semidirect |
| 95. C59 | #7749 | semidirect |
| 116. C2×Q8 | #11745671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425183 | 2 |
| #21421922 | 2 |
| C59×#2811 | 2 |
| #7749 | 59 |