Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D101 | C2 | semidirect |
| 3. #20265492 | C2 | semidirect |
| 4. #20265469 | C2 | semidirect |
| 5. #20265378 | C2 | semidirect |
| 6. #20265377 | C2 | semidirect |
| 7. #20265317 | C2 | semidirect |
| 8. #20265280 | C2 | semidirect |
| 9. #20265276 | C2 | semidirect |
| 10. #20265233 | C2 | semidirect |
| 11. #477×C101 | C2 | semidirect |
| 87. Q8×C101 | #41 | semidirect |
| 113. Dic202 | #41 | semidirect |
| 141. C101 | #3112 | semidirect |
| 146. #477 | D101 | semidirect |
| 231. Q8 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265728 | 2 |
| C4×Q8×D101 | 2 |
| #20265492 | 2 |
| #20265469 | 2 |
| #20265378 | 2 |
| #20265377 | 2 |
| #20265317 | 2 |
| #20265280 | 2 |
| #20265276 | 2 |
| #20265233 | 2 |
| #477×C101 | 2 |
| #3112 | 101 |