Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
398 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21426012 | C2 | semidirect |
| 2. #21425419 | C2 | semidirect |
| 3. #21422105 | C2 | semidirect |
| 4. #21422036 | C2 | semidirect |
| 99. C2×C4×C59 | SD32 | semidirect |
| 155. C59 | #12161 | semidirect |
| 246. C2×C4 | #14273671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426012 | 2 |
| #21425419 | 2 |
| #21422105 | 2 |
| #21422036 | 2 |
| C59×#3245 | 2 |
| #12161 | 59 |