Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21437198 | C2 | semidirect |
| 3. C2×#16837212 | C2 | semidirect |
| 4. #21424152 | C2 | semidirect |
| 5. #21422209 | C2 | semidirect |
| 6. #21422195 | C2 | semidirect |
| 7. C59×#2143 | C2 | semidirect |
| 14. #16837674 | C4 | semidirect |
| 15. #16837669 | C4 | semidirect |
| 176. #2143 | D59 | semidirect |
| 205. C59 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437198 | 2 |
| #21433812 | 2 |
| C2×#16837212 | 2 |
| #21424152 | 2 |
| #21422209 | 2 |
| #21422195 | 2 |
| C59×#2143 | 2 |
| #13070 | 59 |