Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #20265900 | C2 | semidirect |
| 2. #20265539 | C2 | semidirect |
| 3. #20265529 | C2 | semidirect |
| 4. #20265469 | C2 | semidirect |
| 5. #20265454 | C2 | semidirect |
| 7. #20265382 | C2 | semidirect |
| 8. #20265308 | C2 | semidirect |
| 9. #20265277 | C2 | semidirect |
| 11. D4×Q8×C101 | C2 | semidirect |
| 123. C101 | #3367 | semidirect |
| 125. D4×Q8 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265900 | 2 |
| #20265539 | 2 |
| #20265529 | 2 |
| #20265469 | 2 |
| #20265454 | 2 |
| #20265392 | 2 |
| #20265382 | 2 |
| #20265308 | 2 |
| #20265277 | 2 |
| C4×#13108059 | 2 |
| D4×Q8×C101 | 2 |
| #3367 | 101 |