Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21425929 | C2 | semidirect |
| 3. #21422166 | C2 | semidirect |
| 4. #21422052 | C2 | semidirect |
| 5. C8×C16×C59 | C2 | semidirect |
| 47. C16×C59 | D8 | semidirect |
| 61. C8×C59 | M32 | semidirect |
| 80. C8×C16 | D59 | semidirect |
| 95. C59 | #12039 | semidirect |
| 128. C16 | D472 | semidirect |
| 142. C8 | #14273666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425929 | 2 |
| C8×D472 | 2 |
| #21422166 | 2 |
| #21422052 | 2 |
| C8×C16×C59 | 2 |
| #12039 | 59 |