Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
812 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 812 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. C2×#16837541 | C2 | semidirect |
| 3. #21424932 | C2 | semidirect |
| 4. #21424031 | C2 | semidirect |
| 5. #21422664 | C2 | semidirect |
| 6. #21421944 | C2 | semidirect |
| 7. C59×#2436 | C2 | semidirect |
| 236. #2436 | D59 | semidirect |
| 273. C59 | #9948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434844 | 2 |
| C2×#16837541 | 2 |
| #21424932 | 2 |
| #21424031 | 2 |
| #21422664 | 2 |
| #21421944 | 2 |
| C59×#2436 | 2 |
| #9948 | 59 |