Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
692 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#16837713 | C2 | semidirect |
| 2. #21428568 | C2 | semidirect |
| 3. #21424933 | C2 | semidirect |
| 4. #21424183 | C2 | semidirect |
| 5. #21422664 | C2 | semidirect |
| 6. #21421943 | C2 | semidirect |
| 125. C22⋊Dic59 | D8 | semidirect |
| 257. C59 | #9952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837713 | 2 |
| #21428568 | 2 |
| #21424933 | 2 |
| #21424183 | 2 |
| #21422664 | 2 |
| #21421943 | 2 |
| C59×#3186 | 2 |
| #9952 | 59 |