Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
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. #20270025 | C2 | semidirect |
| 2. #20270024 | C2 | semidirect |
| 3. #20270010 | C2 | semidirect |
| 4. #20270009 | C2 | semidirect |
| 5. #20270006 | C2 | semidirect |
| 6. #20269998 | C2 | semidirect |
| 7. #20269997 | C2 | semidirect |
| 8. C2×#16809952 | C2 | semidirect |
| 9. Q16×D211 | C2 | semidirect |
| 10. #20269985 | C2 | semidirect |
| 11. #137×C211 | C2 | semidirect |
| 87. C211 | #578 | semidirect |
| 94. #137 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20270025 | 2 |
| #20270024 | 2 |
| #20270010 | 2 |
| #20270009 | 2 |
| #20270006 | 2 |
| #20269998 | 2 |
| #20269997 | 2 |
| C2×#16809952 | 2 |
| Q16×D211 | 2 |
| #20269985 | 2 |
| #137×C211 | 2 |
| #578 | 211 |