Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21422982 | C2 | semidirect |
| 3. #21422167 | C2 | semidirect |
| 4. #21422057 | C2 | semidirect |
| 5. #21422056 | C2 | semidirect |
| 6. C8×C59⋊C16 | C2 | semidirect |
| 7. C59×#1589 | C2 | semidirect |
| 68. C59⋊C16 | M16 | semidirect |
| 88. C8×C59 | D16 | semidirect |
| 109. #1589 | D59 | semidirect |
| 134. C59 | #12081 | semidirect |
| 201. C8 | #14273668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273668 | 2 |
| #21422982 | 2 |
| #21422167 | 2 |
| #21422057 | 2 |
| #21422056 | 2 |
| C8×C59⋊C16 | 2 |
| C59×#1589 | 2 |
| #12081 | 59 |