Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692277 | C2 | semidirect |
| 2. C2×#15692261 | C2 | semidirect |
| 3. #20265758 | C2 | semidirect |
| 4. #20265436 | C2 | semidirect |
| 5. #20265431 | C2 | semidirect |
| 6. #20265407 | C2 | semidirect |
| 7. #20265176 | C2 | semidirect |
| 8. C2×#106×C101 | C2 | semidirect |
| 55. C2×C8×C101 | D4 | semidirect |
| 106. C101 | #3060 | semidirect |
| 113. C2×#106 | D101 | semidirect |
| 158. C2×C8 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| C2×#15692261 | 2 |
| #20265758 | 2 |
| #20265436 | 2 |
| #20265431 | 2 |
| #20265407 | 2 |
| #20265176 | 2 |
| C2×#106×C101 | 2 |
| #3060 | 101 |