Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. D4×Q8×C13 | C2 | semidirect |
| 2. #11719284 | C2 | semidirect |
| 3. #11718748 | C2 | semidirect |
| 4. #11718745 | C2 | semidirect |
| 5. #11718741 | C2 | semidirect |
| 6. #11718740 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 10. #11718670 | C2 | semidirect |
| 11. #11718669 | C2 | semidirect |
| 62. #6104 | Q8 | semidirect |
| 93. D52 | C2×Q8 | semidirect |
| 99. #1055 | C2×Q8 | semidirect |
| 101. D4×Q8 | D13 | semidirect |
| 194. C13 | #3384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C13 | 2 |
| #11719284 | 2 |
| #11718748 | 2 |
| #11718745 | 2 |
| #11718741 | 2 |
| #11718740 | 2 |
| #11718685 | 2 |
| #11718675 | 2 |
| C4×#6104 | 2 |
| #11718670 | 2 |
| #11718669 | 2 |
| #3384 | 13 |