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. C13×#554 | C2 | semidirect |
| 2. Q8×D52 | C2 | semidirect |
| 3. #11718745 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 5. #11718727 | C2 | semidirect |
| 6. #11718726 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 10. #11718669 | C2 | semidirect |
| 11. #11718668 | C2 | semidirect |
| 63. #6104 | Q8 | semidirect |
| 79. D4×C13 | C2×Q8 | semidirect |
| 99. #1055 | C2×Q8 | semidirect |
| 100. #554 | D13 | semidirect |
| 194. C13 | #3384 | semidirect |
| 204. D4 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#554 | 2 |
| Q8×D52 | 2 |
| #11718745 | 2 |
| #11718740 | 2 |
| #11718727 | 2 |
| #11718726 | 2 |
| #11718685 | 2 |
| #11718675 | 2 |
| C4×#6104 | 2 |
| #11718669 | 2 |
| #11718668 | 2 |
| #3384 | 13 |