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 |
|---|---|---|
| 2. #20265515 | C2 | semidirect |
| 3. #20265469 | C2 | semidirect |
| 4. #20265464 | C2 | semidirect |
| 5. #20265384 | C2 | semidirect |
| 6. #20265379 | C2 | semidirect |
| 8. #20265282 | C2 | semidirect |
| 9. #20265275 | C2 | semidirect |
| 10. #20265234 | C2 | semidirect |
| 11. #533×C101 | C2 | semidirect |
| 137. C101 | #3116 | semidirect |
| 138. #533 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13108074 | 2 |
| #20265515 | 2 |
| #20265469 | 2 |
| #20265464 | 2 |
| #20265384 | 2 |
| #20265379 | 2 |
| #20265337 | 2 |
| #20265282 | 2 |
| #20265275 | 2 |
| #20265234 | 2 |
| #533×C101 | 2 |
| #3116 | 101 |