Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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×#16861626 | C2 | semidirect |
| 2. C22×#14523346 | C2 | semidirect |
| 3. #22551659 | C2 | semidirect |
| 4. #22551649 | C2 | semidirect |
| 5. C22⋊#14523346 | C2 | semidirect |
| 6. C4×#14523346 | C2 | semidirect |
| 24. #14523346 | D4 | semidirect |
| 26. C22⋊D257 | C8 | semidirect |
| 39. C22×C257 | C2×C8 | semidirect |
| 43. C2×D257 | C2×C8 | semidirect |
| 47. Dic257 | C2×C8 | semidirect |
| 55. C257 | C8×D4 | semidirect |
| 98. C22 | #16861626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861626 | 2 |
| C22×#14523346 | 2 |
| #22551659 | 2 |
| #22551649 | 2 |
| C22⋊#14523346 | 2 |
| C4×#14523346 | 2 |
| #22551552 | 2 |
| C8×D4 | 257 |