Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4×C13×Q16 | C2 | semidirect |
| 3. #11718849 | C2 | semidirect |
| 4. #11718682 | C2 | semidirect |
| 5. D13×#107 | C2 | semidirect |
| 6. #11718470 | C2 | semidirect |
| 8. #11718343 | C2 | semidirect |
| 60. D52 | Q16 | semidirect |
| 73. C4×Q16 | D13 | semidirect |
| 132. C13 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719284 | 2 |
| C4×C13×Q16 | 2 |
| #11718849 | 2 |
| #11718682 | 2 |
| D13×#107 | 2 |
| #11718470 | 2 |
| C8×D52 | 2 |
| #11718343 | 2 |
| #3338 | 13 |