Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#88178 | C2 | semidirect |
| 3. C2×#88129 | C2 | semidirect |
| 4. C2×#88123 | C2 | semidirect |
| 5. C4×C13×C22⋊C4 | C2 | semidirect |
| 6. #11718622 | C2 | semidirect |
| 7. #11718600 | C2 | semidirect |
| 8. #11718590 | C2 | semidirect |
| 9. #11718329 | C2 | semidirect |
| 94. C2×C4×C13 | #41 | semidirect |
| 116. C4×C22⋊C4 | D13 | semidirect |
| 206. C13 | #2432 | semidirect |
| 241. C2×C4 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6127 | 2 |
| C2×#88178 | 2 |
| C2×#88129 | 2 |
| C2×#88123 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718622 | 2 |
| #11718600 | 2 |
| #11718590 | 2 |
| #11718329 | 2 |
| #2432 | 13 |