Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 3. #21422167 | C2 | semidirect |
| 4. #21422060 | C2 | semidirect |
| 6. #21422013 | C2 | semidirect |
| 7. C8×Q16×C59 | C2 | semidirect |
| 26. #14273670 | C8 | semidirect |
| 48. Q16×C59 | C2×C8 | semidirect |
| 67. C59⋊C16 | C2×C8 | semidirect |
| 103. C8×Q16 | D59 | semidirect |
| 128. C59 | #12043 | semidirect |
| 154. Q16 | C8×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273670 | 2 |
| C8×D472 | 2 |
| #21422167 | 2 |
| #21422060 | 2 |
| #21422056 | 2 |
| #21422013 | 2 |
| C8×Q16×C59 | 2 |
| #12043 | 59 |