Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15692278 | C2 | semidirect |
| 2. #20265728 | C2 | semidirect |
| 3. C4×#13108075 | C2 | semidirect |
| 4. #20265401 | C2 | semidirect |
| 5. #20265395 | C2 | semidirect |
| 6. #20265379 | C2 | semidirect |
| 7. #20265377 | C2 | semidirect |
| 8. #20265373 | C2 | semidirect |
| 9. C4⋊C8×D101 | C2 | semidirect |
| 10. #20265172 | C2 | semidirect |
| 11. #462×C101 | C2 | semidirect |
| 47. #13108075 | D4 | semidirect |
| 137. C4×C101 | #135 | semidirect |
| 151. C101 | #3035 | semidirect |
| 157. #462 | D101 | semidirect |
| 292. C4 | #15692278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| #20265728 | 2 |
| C4×#13108075 | 2 |
| #20265401 | 2 |
| #20265395 | 2 |
| #20265379 | 2 |
| #20265377 | 2 |
| #20265373 | 2 |
| C4⋊C8×D101 | 2 |
| #20265172 | 2 |
| #462×C101 | 2 |
| #3035 | 101 |