Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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. D16×Dic59 | C2 | semidirect |
| 3. #21425942 | C2 | semidirect |
| 4. #21422297 | C2 | semidirect |
| 5. #21422275 | C2 | semidirect |
| 6. #21422229 | C2 | semidirect |
| 7. C59×#1415 | C2 | semidirect |
| 11. #16837237 | C4 | semidirect |
| 24. D944 | C2×C4 | semidirect |
| 30. C59⋊C32 | C2×C4 | semidirect |
| 33. D16×C59 | C2×C4 | semidirect |
| 90. #1415 | D59 | semidirect |
| 109. C59 | #13654 | semidirect |
| 117. D16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837237 | 2 |
| D16×Dic59 | 2 |
| #21425942 | 2 |
| #21422297 | 2 |
| #21422275 | 2 |
| #21422229 | 2 |
| C59×#1415 | 2 |
| #13654 | 59 |