Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265849 | C2 | semidirect |
| 2. #20265543 | C2 | semidirect |
| 3. #20265525 | C2 | semidirect |
| 4. #20265474 | C2 | semidirect |
| 5. #20265464 | C2 | semidirect |
| 6. #20265372 | C2 | semidirect |
| 7. #20265372 | C2 | semidirect |
| 8. #20265308 | C2 | semidirect |
| 9. #20265287 | C2 | semidirect |
| 10. C4×#13108059 | C2 | semidirect |
| 11. #554×C101 | C2 | semidirect |
| 80. D4×C101 | #41 | semidirect |
| 130. C101 | #3366 | semidirect |
| 131. #554 | D101 | semidirect |
| 218. D4 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265849 | 2 |
| #20265543 | 2 |
| #20265525 | 2 |
| #20265474 | 2 |
| #20265464 | 2 |
| #20265372 | 2 |
| #20265308 | 2 |
| #20265287 | 2 |
| C4×#13108059 | 2 |
| #554×C101 | 2 |
| #3366 | 101 |