Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15692275 | C2 | semidirect |
| 2. #20265848 | C2 | semidirect |
| 3. #20265551 | C2 | semidirect |
| 4. #20265408 | C2 | semidirect |
| 5. #20265384 | C2 | semidirect |
| 6. #20265372 | C2 | semidirect |
| 7. #20265337 | C2 | semidirect |
| 8. #20265322 | C2 | semidirect |
| 9. C4×#13108062 | C2 | semidirect |
| 10. D4×#11717579 | C2 | semidirect |
| 11. #547×C101 | C2 | semidirect |
| 52. #13108062 | D4 | semidirect |
| 129. C4×C101 | #135 | semidirect |
| 141. C101 | #3284 | semidirect |
| 144. #547 | D101 | semidirect |
| 272. C4 | #15692275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692275 | 2 |
| #20265848 | 2 |
| #20265551 | 2 |
| #20265408 | 2 |
| #20265384 | 2 |
| #20265372 | 2 |
| #20265337 | 2 |
| #20265322 | 2 |
| C4×#13108062 | 2 |
| D4×#11717579 | 2 |
| #547×C101 | 2 |
| #3284 | 101 |