Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20265728 | C2 | semidirect |
| 2. C4×#13108075 | C2 | semidirect |
| 3. #20265503 | C2 | semidirect |
| 4. #20265454 | C2 | semidirect |
| 5. #20265377 | C2 | semidirect |
| 6. #20265373 | C2 | semidirect |
| 7. #20265325 | C2 | semidirect |
| 8. #20265288 | C2 | semidirect |
| 9. #20265280 | C2 | semidirect |
| 10. #20265233 | C2 | semidirect |
| 11. #475×C101 | C2 | semidirect |
| 88. Q8×C101 | #41 | semidirect |
| 106. D404 | #41 | semidirect |
| 145. C101 | #3115 | semidirect |
| 149. #475 | D101 | semidirect |
| 233. 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×#13108075 | 2 |
| #20265503 | 2 |
| #20265454 | 2 |
| #20265377 | 2 |
| #20265373 | 2 |
| #20265325 | 2 |
| #20265288 | 2 |
| #20265280 | 2 |
| #20265233 | 2 |
| #475×C101 | 2 |
| #3115 | 101 |