Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 2. #10623074 | C2 | semidirect |
| 3. C8×D4×C11 | C2 | semidirect |
| 4. #10622727 | C2 | semidirect |
| 5. C2×#66881 | C2 | semidirect |
| 6. #10622464 | C2 | semidirect |
| 7. #10622455 | C2 | semidirect |
| 8. #10622348 | C2 | semidirect |
| 9. #10622334 | C2 | semidirect |
| 10. C4×#4314 | C2 | semidirect |
| 11. #10622293 | C2 | semidirect |
| 77. D4×C11 | SD16 | semidirect |
| 101. C8×C11 | #41 | semidirect |
| 111. C8×D4 | D11 | semidirect |
| 197. C11 | #3335 | semidirect |
| 207. D4 | #4314 | semidirect |
| 224. C8 | #4341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623086 | 2 |
| #10623074 | 2 |
| C8×D4×C11 | 2 |
| #10622727 | 2 |
| C2×#66881 | 2 |
| #10622464 | 2 |
| #10622455 | 2 |
| #10622348 | 2 |
| #10622334 | 2 |
| C4×#4314 | 2 |
| #10622293 | 2 |
| #3335 | 11 |