Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
308 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C13 |
| prime radical | D42×C13 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#486 | C2 | semidirect |
| 3. C13×#474 | C2 | semidirect |
| 4. C13×#461 | C2 | semidirect |
| 5. C13×#331 | C2 | semidirect |
| 6. C13×D4⋊C8 | C2 | semidirect |
| 7. C13×D4⋊C8 | C2 | semidirect |
| 11. C13×C4⋊Q8 | C22 | semidirect |
| 19. C13×C4⋊C8 | C22 | semidirect |
| 20. C13×C4⋊C8 | C22 | semidirect |
| 24. C4×C8×C13 | C22 | semidirect |
| 52. #1639 | C13 | direct (N × H) |
| 71. D4×C13 | SD16 | semidirect |
| 86. #486 | C2×C13 | semidirect |
| 87. #474 | C2×C13 | semidirect |
| 88. #461 | C2×C13 | semidirect |
| 89. #331 | C2×C13 | semidirect |
| 90. D4⋊C8 | C2×C13 | semidirect |
| 91. D4⋊C8 | C2×C13 | semidirect |
| 114. C4⋊Q8 | C22×C13 | semidirect |
| 122. C4⋊C8 | C22×C13 | semidirect |
| 123. C4⋊C8 | C22×C13 | semidirect |
| 127. C4×C8 | C22×C13 | semidirect |
| 161. C13 | #1639 | direct (N × H) |
| 180. D4 | C13×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D42×C13 | 2 |
| C13×#486 | 2 |
| C13×#474 | 2 |
| C13×#461 | 2 |
| C13×#331 | 2 |
| C13×D4⋊C8 | 2 |
| #1639 | 13 |