Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20265727 | C2 | semidirect |
| 2. #20265580 | C2 | semidirect |
| 3. #20265553 | C2 | semidirect |
| 4. #20265525 | C2 | semidirect |
| 5. #20265523 | C2 | semidirect |
| 6. #20265411 | C2 | semidirect |
| 7. C4×#13108059 | C2 | semidirect |
| 8. C2×C4×#11717579 | C2 | semidirect |
| 9. #532×C101 | C2 | semidirect |
| 80. C2×C4×C101 | D8 | semidirect |
| 95. #11717579 | #41 | semidirect |
| 121. C101 | #3169 | semidirect |
| 123. #532 | D101 | semidirect |
| 208. C2×C4 | #13108059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265727 | 2 |
| #20265580 | 2 |
| #20265553 | 2 |
| #20265525 | 2 |
| #20265523 | 2 |
| #20265411 | 2 |
| C4×#13108059 | 2 |
| C2×C4×#11717579 | 2 |
| #532×C101 | 2 |
| #3169 | 101 |