Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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×#15692261 | C2 | semidirect |
| 3. #20265256 | C2 | semidirect |
| 4. C8×D404 | C2 | semidirect |
| 5. #20265201 | C2 | semidirect |
| 6. #20265143 | C2 | semidirect |
| 7. C2×C4×C8×C101 | C2 | semidirect |
| 41. C2×C8×C101 | D4 | semidirect |
| 75. C4×C101 | #131 | semidirect |
| 84. C101 | #2931 | semidirect |
| 91. C2×C4×C8 | D101 | semidirect |
| 123. C2×C8 | D404 | semidirect |
| 160. C4 | #15692261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692261 | 2 |
| #20265727 | 2 |
| #20265256 | 2 |
| C8×D404 | 2 |
| #20265201 | 2 |
| #20265143 | 2 |
| C2×C4×C8×C101 | 2 |
| #2931 | 101 |