Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. #20265900 | C2 | semidirect |
| 2. Q8×D404 | C2 | semidirect |
| 3. #20265537 | C2 | semidirect |
| 4. #20265528 | C2 | semidirect |
| 5. #20265473 | C2 | semidirect |
| 6. #20265458 | C2 | semidirect |
| 8. #20265383 | C2 | semidirect |
| 9. #20265279 | C2 | semidirect |
| 11. #446×C101 | C2 | semidirect |
| 123. C101 | #3367 | semidirect |
| 132. #446 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265900 | 2 |
| Q8×D404 | 2 |
| #20265537 | 2 |
| #20265528 | 2 |
| #20265473 | 2 |
| #20265458 | 2 |
| #20265393 | 2 |
| #20265383 | 2 |
| #20265279 | 2 |
| C4×D808 | 2 |
| #446×C101 | 2 |
| #3367 | 101 |