Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20265893 | C2 | semidirect |
| 2. #20265830 | C2 | semidirect |
| 3. #20265503 | C2 | semidirect |
| 4. #20265497 | C2 | semidirect |
| 5. #20265464 | C2 | semidirect |
| 6. #20265454 | C2 | semidirect |
| 7. #20265431 | C2 | semidirect |
| 8. C4×D808 | C2 | semidirect |
| 9. #20265256 | C2 | semidirect |
| 10. #20265216 | C2 | semidirect |
| 11. #498×C101 | C2 | semidirect |
| 100. C8×C101 | #41 | semidirect |
| 128. C101 | #3354 | semidirect |
| 131. #498 | D101 | semidirect |
| 229. C8 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265893 | 2 |
| #20265830 | 2 |
| #20265503 | 2 |
| #20265497 | 2 |
| #20265464 | 2 |
| #20265454 | 2 |
| #20265431 | 2 |
| C4×D808 | 2 |
| #20265256 | 2 |
| #20265216 | 2 |
| #498×C101 | 2 |
| #3354 | 101 |