Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 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. #20265905 | C2 | semidirect |
| 4. #20265557 | C2 | semidirect |
| 6. #20265387 | C2 | semidirect |
| 7. #20265386 | C2 | semidirect |
| 9. #20265307 | C2 | semidirect |
| 10. #20265283 | C2 | semidirect |
| 120. C101 | #3398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265905 | 2 |
| #20265897 | 2 |
| #20265568 | 2 |
| #20265557 | 2 |
| #20265398 | 2 |
| #20265387 | 2 |
| #20265386 | 2 |
| #20265382 | 2 |
| #20265307 | 2 |
| #20265283 | 2 |
| C4×SD16×C101 | 2 |
| #3398 | 101 |