Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20265554 | C2 | semidirect |
| 3. #20265525 | C2 | semidirect |
| 4. #20265414 | C2 | semidirect |
| 5. #20265259 | C2 | semidirect |
| 6. C4×C8×D101 | C2 | semidirect |
| 7. #500×C101 | C2 | semidirect |
| 63. C4×D101 | D8 | semidirect |
| 64. C8×C101 | #41 | semidirect |
| 86. C101 | #3169 | semidirect |
| 88. #500 | D101 | semidirect |
| 151. C8 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265728 | 2 |
| #20265554 | 2 |
| #20265525 | 2 |
| #20265414 | 2 |
| #20265259 | 2 |
| C4×C8×D101 | 2 |
| #500×C101 | 2 |
| #3169 | 101 |