Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20265888 | C2 | semidirect |
| 2. #20265847 | C2 | semidirect |
| 3. #20265540 | C2 | semidirect |
| 4. #20265475 | C2 | semidirect |
| 5. #20265464 | C2 | semidirect |
| 6. #20265371 | C2 | semidirect |
| 7. #20265369 | C2 | semidirect |
| 8. #20265307 | C2 | semidirect |
| 9. #20265286 | C2 | semidirect |
| 10. C4×D808 | C2 | semidirect |
| 11. #486×C101 | C2 | semidirect |
| 96. D404 | #41 | semidirect |
| 130. C101 | #3366 | semidirect |
| 134. #486 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265888 | 2 |
| #20265847 | 2 |
| #20265540 | 2 |
| #20265475 | 2 |
| #20265464 | 2 |
| #20265371 | 2 |
| #20265369 | 2 |
| #20265307 | 2 |
| #20265286 | 2 |
| C4×D808 | 2 |
| #486×C101 | 2 |
| #3366 | 101 |