Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #20265521 | C2 | semidirect |
| 4. #20265520 | C2 | semidirect |
| 5. #20265514 | C2 | semidirect |
| 6. #20265509 | C2 | semidirect |
| 7. #20265220 | C2 | semidirect |
| 8. #20265185 | C2 | semidirect |
| 9. C2×#15692180 | C2 | semidirect |
| 11. #427×C101 | C2 | semidirect |
| 127. C101 | #3097 | semidirect |
| 135. #427 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265753 | 2 |
| #20265657 | 2 |
| #20265521 | 2 |
| #20265520 | 2 |
| #20265514 | 2 |
| #20265509 | 2 |
| #20265220 | 2 |
| #20265185 | 2 |
| C2×#15692180 | 2 |
| #20265143 | 2 |
| #427×C101 | 2 |
| #3097 | 101 |