Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
780 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 140 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. C22×C4⋊#261 | C2 | semidirect |
| 4. C2×(C2×#261)⋊C4 | C2 | semidirect |
| 5. C2×(C2×#261)⋊C4 | C2 | semidirect |
| 16. C2×C13×C22⋊C4 | C4 | semidirect |
| 17. C2×C22⋊Dic13 | C4 | semidirect |
| 18. C2×#6103 | C4 | semidirect |
| 19. C2×#6103 | C4 | semidirect |
| 74. C23×C13 | C4⋊C4 | semidirect |
| 98. C22×D13 | C4⋊C4 | semidirect |
| 126. C2×C4×C13 | C22⋊C4 | semidirect |
| 130. C2×Dic13 | C22⋊C4 | semidirect |
| 202. C2×C22⋊C4 | #261 | semidirect |
| 263. C13 | #1439 | semidirect |
| 301. C23 | C4⋊#261 | semidirect |
| 330. C2×C4 | C22⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#261 | 2 |
| C22×C4⋊#261 | 2 |
| C2×C22⋊C4×D13 | 2 |
| C2×(C2×#261)⋊C4 | 2 |
| #1439 | 13 |