Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20265724 | C2 | semidirect |
| 2. #20265581 | C2 | semidirect |
| 3. #20265552 | C2 | semidirect |
| 4. #20265522 | C2 | semidirect |
| 5. #20265414 | C2 | semidirect |
| 6. #20265412 | C2 | semidirect |
| 7. #20265410 | C2 | semidirect |
| 8. C4×D808 | C2 | semidirect |
| 9. C4×#13108059 | C2 | semidirect |
| 10. C4×C8×D101 | C2 | semidirect |
| 11. C4×D8×C101 | C2 | semidirect |
| 96. C4×D101 | D8 | semidirect |
| 99. C8×C101 | #41 | semidirect |
| 101. #11717579 | #41 | semidirect |
| 128. C101 | #3169 | semidirect |
| 138. C4×D8 | D101 | semidirect |
| 229. C8 | #13108074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265724 | 2 |
| #20265581 | 2 |
| #20265552 | 2 |
| #20265522 | 2 |
| #20265414 | 2 |
| #20265412 | 2 |
| #20265410 | 2 |
| C4×D808 | 2 |
| C4×#13108059 | 2 |
| C4×C8×D101 | 2 |
| C4×D8×C101 | 2 |
| #3169 | 101 |