Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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. #20265660 | C2 | semidirect |
| 2. #20265515 | C2 | semidirect |
| 3. #20265510 | C2 | semidirect |
| 4. #20265498 | C2 | semidirect |
| 5. #20265488 | C2 | semidirect |
| 6. #20265217 | C2 | semidirect |
| 7. C2×#15692188 | C2 | semidirect |
| 8. #20265178 | C2 | semidirect |
| 9. #20265173 | C2 | semidirect |
| 10. #20265144 | C2 | semidirect |
| 134. C101 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265660 | 2 |
| #20265515 | 2 |
| #20265510 | 2 |
| #20265498 | 2 |
| #20265488 | 2 |
| #20265217 | 2 |
| C2×#15692188 | 2 |
| #20265178 | 2 |
| #20265173 | 2 |
| #20265144 | 2 |
| #537×C101 | 2 |
| #3098 | 101 |