Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21425237 | C2 | semidirect |
| 2. #21425232 | C2 | semidirect |
| 3. #21425178 | C2 | semidirect |
| 4. #21421922 | C2 | semidirect |
| 5. #21421917 | C2 | semidirect |
| 6. #21421917 | C2 | semidirect |
| 68. C2×Q8×C59 | SD16 | semidirect |
| 253. C59 | #7781 | semidirect |
| 301. C2×Q8 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425237 | 2 |
| #21425232 | 2 |
| #21425178 | 2 |
| #21421922 | 2 |
| #21421917 | 2 |
| C59×#2733 | 2 |
| #7781 | 59 |