Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15692276 | C2 | semidirect |
| 2. #20265847 | C2 | semidirect |
| 3. #20265830 | C2 | semidirect |
| 4. #20265403 | C2 | semidirect |
| 5. #20265384 | C2 | semidirect |
| 6. #20265369 | C2 | semidirect |
| 7. #20265336 | C2 | semidirect |
| 8. #20265321 | C2 | semidirect |
| 9. C4×#13108063 | C2 | semidirect |
| 10. C8×D404 | C2 | semidirect |
| 11. #492×C101 | C2 | semidirect |
| 57. #13108063 | D4 | semidirect |
| 127. C4×C101 | #135 | semidirect |
| 141. C101 | #3284 | semidirect |
| 145. #492 | D101 | semidirect |
| 272. C4 | #15692276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692276 | 2 |
| #20265847 | 2 |
| #20265830 | 2 |
| #20265403 | 2 |
| #20265384 | 2 |
| #20265369 | 2 |
| #20265336 | 2 |
| #20265321 | 2 |
| C4×#13108063 | 2 |
| C8×D404 | 2 |
| #492×C101 | 2 |
| #3284 | 101 |