Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 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 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C22×C13×#41 | C2 |
| hypercenter | C22×#41 | D13 |
| hypocenter | C13 | #3487 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13×#41 | C2 | semidirect |
| 2. C2×#88254 | C2 | semidirect |
| 3. #11719539 | C2 | semidirect |
| 4. #11719536 | C2 | semidirect |
| 5. #11719517 | C2 | semidirect |
| 6. #11719510 | C2 | semidirect |
| 7. #11719496 | C2 | semidirect |
| 14. C2×#6131 | C22 | semidirect |
| 15. C2×Q8×D13 | C22 | semidirect |
| 18. Q8×Dic13 | C22 | semidirect |
| 19. #88194 | C22 | semidirect |
| 20. #88192 | C22 | semidirect |
| 21. #88190 | C22 | semidirect |
| 22. #88184 | C22 | semidirect |
| 24. C4×C22⋊D13 | C22 | semidirect |
| 26. #88178 | C22 | semidirect |
| 29. C2×Q8×C13 | D4 | semidirect |
| 72. C22×#41 | D13 | semidirect |
| 120. C2×Q8 | C22⋊D13 | semidirect |
| 138. C13 | #3487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×#41 | 2 |
| C2×#88254 | 2 |
| #11719539 | 2 |
| #11719536 | 2 |
| #11719517 | 2 |
| #11719510 | 2 |
| #11719496 | 2 |
| #3487 | 13 |