Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#15692287 | C2 | semidirect |
| 3. C4×Q8×D101 | C2 | semidirect |
| 4. #20265402 | C2 | semidirect |
| 5. #20265401 | C2 | semidirect |
| 6. #20265384 | C2 | semidirect |
| 7. #20265378 | C2 | semidirect |
| 8. #20265377 | C2 | semidirect |
| 9. #20265199 | C2 | semidirect |
| 10. #20265177 | C2 | semidirect |
| 11. #462×C101 | C2 | semidirect |
| 49. Q8×D101 | D4 | semidirect |
| 133. C4×C101 | #137 | semidirect |
| 147. C101 | #3037 | semidirect |
| 154. #462 | D101 | semidirect |
| 285. C4 | #15692287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692287 | 2 |
| #20265728 | 2 |
| C4×Q8×D101 | 2 |
| #20265402 | 2 |
| #20265401 | 2 |
| #20265384 | 2 |
| #20265378 | 2 |
| #20265377 | 2 |
| #20265199 | 2 |
| #20265177 | 2 |
| #462×C101 | 2 |
| #3037 | 101 |