Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#261 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting, prime radical | C2×C13×#41 | C4 |
| cosocle | C2×Dic13 | C24 |
| hypercenter | C2×#41 | #261 |
| hypocenter | C13 | #2990 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11719158 | C2 | semidirect |
| 3. #11719144 | C2 | semidirect |
| 4. D4×#1057 | C2 | semidirect |
| 5. #11719129 | C2 | semidirect |
| 6. #11719128 | C2 | semidirect |
| 7. #11719125 | C2 | semidirect |
| 8. C2×#88112 | C2 | semidirect |
| 65. D4×C13 | M16 | semidirect |
| 167. C13 | #2990 | semidirect |
| 172. D4 | #6122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic13 | 2 |
| #11719158 | 2 |
| #11719144 | 2 |
| D4×#1057 | 2 |
| #11719129 | 2 |
| #11719128 | 2 |
| #11719125 | 2 |
| C2×#88112 | 2 |
| #2990 | 13 |