Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13108062 | C2 | semidirect |
| 2. C22×#13108059 | C2 | semidirect |
| 3. C2×#15692243 | C2 | semidirect |
| 4. #20265564 | C2 | direct (N × H) |
| 5. C2×#15692166 | C2 | semidirect |
| 6. C2×#127×C101 | C2 | semidirect |
| 10. C2×#13108062 | C22 | semidirect |
| 12. C2×#13108059 | C22 | semidirect |
| 15. #15692243 | C22 | semidirect |
| 17. #15692166 | C22 | semidirect |
| 21. #127×C101 | C22 | semidirect |
| 33. C2×#11717579 | D4 | semidirect |
| 69. #11717579 | C2×D4 | semidirect |
| 84. C2×C101 | #496 | semidirect |
| 89. C101 | C2×#496 | semidirect |
| 92. C2×#127 | D101 | semidirect |
| 106. #127 | C2×D101 | semidirect |
| 174. C2 | #20265564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108062 | 2 |
| C22×#13108059 | 2 |
| C2×#15692243 | 2 |
| #20265564 | 2 |
| C2×#15692166 | 2 |
| C2×#127×C101 | 2 |
| C2×#496 | 101 |