Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21440008 | C2 | semidirect |
| 2. #21440007 | C2 | semidirect |
| 3. #21439993 | C2 | semidirect |
| 4. #21439992 | C2 | semidirect |
| 5. #21439989 | C2 | semidirect |
| 6. #21439981 | C2 | semidirect |
| 7. #21439980 | C2 | semidirect |
| 8. C2×#16838538 | C2 | semidirect |
| 9. Q16×D239 | C2 | semidirect |
| 10. #21439968 | C2 | semidirect |
| 11. #137×C239 | C2 | semidirect |
| 87. C239 | #578 | semidirect |
| 94. #137 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440008 | 2 |
| #21440007 | 2 |
| #21439993 | 2 |
| #21439992 | 2 |
| #21439989 | 2 |
| #21439981 | 2 |
| #21439980 | 2 |
| C2×#16838538 | 2 |
| Q16×D239 | 2 |
| #21439968 | 2 |
| #137×C239 | 2 |
| #578 | 239 |