Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
504 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21425430 | C2 | semidirect |
| 3. #21425237 | C2 | semidirect |
| 5. #21421918 | C2 | semidirect |
| 7. C59×#1272 | C2 | semidirect |
| 67. C2×Q8×C59 | SD16 | semidirect |
| 203. #1272 | D59 | semidirect |
| 233. C59 | #7753 | semidirect |
| 280. C2×Q8 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21431114 | 2 |
| #21425430 | 2 |
| #21425237 | 2 |
| #21425181 | 2 |
| #21421918 | 2 |
| #21421916 | 2 |
| C59×#1272 | 2 |
| #7753 | 59 |