Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265905 | C2 | semidirect |
| 4. #20265528 | C2 | semidirect |
| 5. #20265485 | C2 | semidirect |
| 8. #20265388 | C2 | semidirect |
| 9. C4×Dic404 | C2 | semidirect |
| 11. C8×Q8×C101 | C2 | semidirect |
| 116. C101 | #3364 | semidirect |
| 125. C8×Q8 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265905 | 2 |
| #20265900 | 2 |
| #20265532 | 2 |
| #20265528 | 2 |
| #20265485 | 2 |
| #20265458 | 2 |
| #20265400 | 2 |
| #20265388 | 2 |
| C4×Dic404 | 2 |
| C4×#13108063 | 2 |
| C8×Q8×C101 | 2 |
| #3364 | 101 |