Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20265573 | C2 | semidirect |
| 4. #20265527 | C2 | semidirect |
| 6. #20264898 | C2 | semidirect |
| 7. #500×C101 | C2 | semidirect |
| 52. C8×C101 | SD16 | semidirect |
| 70. C101 | #1714 | semidirect |
| 71. #500 | D101 | semidirect |
| 124. C8 | #13108061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265573 | 2 |
| #20265551 | 2 |
| #20265550 | 2 |
| #20265527 | 2 |
| #20265525 | 2 |
| #20264898 | 2 |
| #500×C101 | 2 |
| #1714 | 101 |