Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
614 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 614 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 |
|---|---|---|
| 2. C2×#16837602 | C2 | semidirect |
| 3. #21422765 | C2 | semidirect |
| 4. #21422495 | C2 | semidirect |
| 5. #21422420 | C2 | semidirect |
| 6. #21421991 | C2 | semidirect |
| 7. C59×#3037 | C2 | semidirect |
| 90. C2×Q8×C59 | D8 | semidirect |
| 216. #3037 | D59 | semidirect |
| 252. C59 | #10177 | semidirect |
| 312. C2×Q8 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435011 | 2 |
| C2×#16837602 | 2 |
| #21422765 | 2 |
| #21422495 | 2 |
| #21422420 | 2 |
| #21421991 | 2 |
| C59×#3037 | 2 |
| #10177 | 59 |