Finite Group DatabasebetaFinite Group DatabasebetaOrder 5408.
366 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 57 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. #72229039 | C2 | semidirect |
| 3. #72214177 | C2 | semidirect |
| 4. #72214162 | C2 | semidirect |
| 5. C2×D13⋊#261 | C2 | semidirect |
| 7. C22×C13×D13 | C4 | semidirect |
| 9. C2×D132 | C4 | semidirect |
| 12. C2×#10621729 | C22 | semidirect |
| 13. C2×#10621728 | C22 | semidirect |
| 15. C22×C132 | C2×C4 | semidirect |
| 17. C2×C13⋊D13 | C2×C4 | semidirect |
| 21. C2×C13×D13 | C2×C4 | semidirect |
| 33. C13×D13 | C22⋊C4 | semidirect |
| 40. C132 | C2×C22⋊C4 | semidirect |
| 49. C22×D13 | #261 | semidirect |
| 58. C22×C13 | C2×#261 | semidirect |
| 71. C2×D13 | C2×#261 | semidirect |
| 87. D13 | C22⋊#261 | semidirect |
| 94. C13 | C2×C22⋊#261 | semidirect |
| 113. C22 | D13⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D132 | 2 |
| #72229039 | 2 |
| #72214177 | 2 |
| #72214162 | 2 |
| C2×D13⋊#261 | 2 |
| C2×C22⋊#261 | 13 |