Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #20265658 | C2 | semidirect |
| 3. #20265521 | C2 | semidirect |
| 4. #20265509 | C2 | semidirect |
| 5. #20265503 | C2 | semidirect |
| 6. #20265497 | C2 | semidirect |
| 7. #20265217 | C2 | semidirect |
| 8. #20265176 | C2 | semidirect |
| 9. #20265174 | C2 | semidirect |
| 10. #20265143 | C2 | semidirect |
| 11. C2×#106×C101 | C2 | semidirect |
| 134. C101 | #3099 | semidirect |
| 142. C2×#106 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265758 | 2 |
| #20265658 | 2 |
| #20265521 | 2 |
| #20265509 | 2 |
| #20265503 | 2 |
| #20265497 | 2 |
| #20265217 | 2 |
| #20265176 | 2 |
| #20265174 | 2 |
| #20265143 | 2 |
| C2×#106×C101 | 2 |
| #3099 | 101 |