Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×#13182017 | C2 | semidirect |
| 2. C22×#13182014 | C2 | semidirect |
| 3. C2×#16812687 | C2 | semidirect |
| 4. #20295413 | C2 | direct (N × H) |
| 5. C2×#16812610 | C2 | semidirect |
| 6. C2×#127×C109 | C2 | semidirect |
| 10. C2×#13182017 | C22 | semidirect |
| 12. C2×#13182014 | C22 | semidirect |
| 15. #16812687 | C22 | semidirect |
| 17. #16812610 | C22 | semidirect |
| 21. #127×C109 | C22 | semidirect |
| 33. C2×#11724784 | D4 | semidirect |
| 69. #11724784 | C2×D4 | semidirect |
| 84. C2×C109 | #496 | semidirect |
| 89. C109 | C2×#496 | semidirect |
| 92. C2×#127 | D109 | semidirect |
| 106. #127 | C2×D109 | semidirect |
| 174. C2 | #20295413 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182017 | 2 |
| C22×#13182014 | 2 |
| C2×#16812687 | 2 |
| #20295413 | 2 |
| C2×#16812610 | 2 |
| C2×#127×C109 | 2 |
| C2×#496 | 109 |