Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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. C8×Q8×C11 | C2 | semidirect |
| 4. Q8⋊(C11⋊C8) | C2 | semidirect |
| 6. #10622117 | C2 | semidirect |
| 7. #10622092 | C2 | semidirect |
| 44. Q8×C11 | M16 | semidirect |
| 62. C8×Q8 | D11 | semidirect |
| 118. C11 | #1588 | semidirect |
| 121. Q8 | #4313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C11 | 2 |
| C4×#4325 | 2 |
| #10622301 | 2 |
| Q8⋊(C11⋊C8) | 2 |
| #10622121 | 2 |
| #10622117 | 2 |
| #10622092 | 2 |
| #1588 | 11 |