Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20265728 | C2 | semidirect |
| 2. #20265712 | C2 | semidirect |
| 3. #20265566 | C2 | semidirect |
| 4. #20265543 | C2 | semidirect |
| 5. #20265539 | C2 | semidirect |
| 6. #20265431 | C2 | semidirect |
| 7. #20265424 | C2 | semidirect |
| 8. #20265264 | C2 | semidirect |
| 9. #20265259 | C2 | semidirect |
| 10. #20265129 | C2 | semidirect |
| 11. #501×C101 | C2 | semidirect |
| 109. C8×C101 | #41 | semidirect |
| 138. C101 | #3171 | semidirect |
| 141. #501 | D101 | semidirect |
| 248. C8 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265728 | 2 |
| #20265712 | 2 |
| #20265566 | 2 |
| #20265543 | 2 |
| #20265539 | 2 |
| #20265431 | 2 |
| #20265424 | 2 |
| #20265264 | 2 |
| #20265259 | 2 |
| #20265129 | 2 |
| #501×C101 | 2 |
| #3171 | 101 |