Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 512 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. C2×#88124 | C2 | semidirect |
| 4. #11718871 | C2 | semidirect |
| 5. #11718641 | C2 | semidirect |
| 6. #11718614 | C2 | semidirect |
| 7. #11718610 | C2 | semidirect |
| 8. #11718598 | C2 | semidirect |
| 143. C13 | #2633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| C2×#88124 | 2 |
| #11718883 | 2 |
| #11718871 | 2 |
| #11718641 | 2 |
| #11718614 | 2 |
| #11718610 | 2 |
| #11718598 | 2 |
| #2633 | 13 |