Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. C13×#499 | C2 | semidirect |
| 3. #11718726 | C2 | semidirect |
| 6. #11718539 | C2 | semidirect |
| 7. #11718535 | C2 | semidirect |
| 9. #11718517 | C2 | semidirect |
| 11. #11718343 | C2 | semidirect |
| 66. #6094 | Q8 | semidirect |
| 67. C8×D13 | Q8 | semidirect |
| 95. #499 | D13 | semidirect |
| 175. C13 | #3164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719394 | 2 |
| C13×#499 | 2 |
| #11718726 | 2 |
| #11718541 | 2 |
| D13×#107 | 2 |
| #11718539 | 2 |
| #11718535 | 2 |
| #11718522 | 2 |
| #11718517 | 2 |
| #11718350 | 2 |
| #11718343 | 2 |
| #3164 | 13 |