Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator | C22×C13 | C23×C4 |
| Fitting | C13×#380 | C2 |
| socle, cosocle | C23×C13 | C24 |
| prime radical | C2×#88184 | C2 |
| hypercenter | #380 | D13 |
| hypocenter | C13 | #2377 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#380 | C2 | semidirect |
| 3. #11718872 | C2 | semidirect |
| 4. #11718651 | C2 | semidirect |
| 5. #11718650 | C2 | semidirect |
| 6. #11718618 | C2 | semidirect |
| 7. #11718617 | C2 | semidirect |
| 8. #11718326 | C2 | semidirect |
| 9. #11718314 | C2 | semidirect |
| 18. #88184 | C4 | semidirect |
| 35. C22×C4×C13 | C2×C4 | semidirect |
| 42. C2×C22⋊D13 | C2×C4 | semidirect |
| 58. #6103 | C2×C4 | semidirect |
| 59. C4⋊Dic13 | C2×C4 | semidirect |
| 107. #380 | D13 | semidirect |
| 175. C22×C4 | C4×D13 | semidirect |
| 191. C13 | #2377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88184 | 2 |
| C13×#380 | 2 |
| #11718872 | 2 |
| #11718651 | 2 |
| #11718650 | 2 |
| #11718618 | 2 |
| #11718617 | 2 |
| #11718326 | 2 |
| #11718314 | 2 |
| #2377 | 13 |