Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20265722 | C2 | semidirect |
| 2. #20265581 | C2 | semidirect |
| 3. #20265552 | C2 | semidirect |
| 4. #20265522 | C2 | semidirect |
| 5. #20265413 | C2 | semidirect |
| 6. #20265411 | C2 | semidirect |
| 7. D8×Dic101 | C2 | semidirect |
| 8. #20265259 | C2 | semidirect |
| 9. #20265257 | C2 | semidirect |
| 10. C2×C8×Dic101 | C2 | semidirect |
| 11. #466×C101 | C2 | semidirect |
| 89. C2×Dic101 | D8 | semidirect |
| 99. C8×C101 | #41 | semidirect |
| 101. #11717579 | #41 | semidirect |
| 128. C101 | #3169 | semidirect |
| 135. #466 | D101 | semidirect |
| 229. C8 | #13108073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265722 | 2 |
| #20265581 | 2 |
| #20265552 | 2 |
| #20265522 | 2 |
| #20265413 | 2 |
| #20265411 | 2 |
| D8×Dic101 | 2 |
| #20265259 | 2 |
| #20265257 | 2 |
| C2×C8×Dic101 | 2 |
| #466×C101 | 2 |
| #3169 | 101 |