Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
648 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#16837797 | C2 | semidirect |
| 2. C2×#16837761 | C2 | semidirect |
| 3. #21425068 | C2 | semidirect |
| 4. C2×#16837142 | C2 | semidirect |
| 5. C2×#16837142 | C2 | semidirect |
| 6. #21421977 | C2 | semidirect |
| 42. #14273727 | D4 | semidirect |
| 51. #14273638 | D4 | semidirect |
| 52. #14273638 | D4 | semidirect |
| 241. C59 | #10081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837797 | 2 |
| C2×#16837761 | 2 |
| #21425068 | 2 |
| C2×#16837142 | 2 |
| #21421977 | 2 |
| C59×#2819 | 2 |
| #10081 | 59 |