Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21424910 | C2 | semidirect |
| 3. #21424262 | C2 | semidirect |
| 4. C2×#16837142 | C2 | semidirect |
| 5. C2×#16837141 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C59×#1959 | C2 | semidirect |
| 54. #14273638 | D4 | semidirect |
| 231. #1959 | D59 | semidirect |
| 266. C59 | #10424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432141 | 2 |
| #21424910 | 2 |
| #21424262 | 2 |
| C2×#16837142 | 2 |
| C2×#16837141 | 2 |
| #21421978 | 2 |
| C59×#1959 | 2 |
| #10424 | 59 |