Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
520 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 185 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. C2×#16812707 | C2 | semidirect |
| 2. C22×C8×D109 | C2 | semidirect |
| 4. #20295096 | C2 | semidirect |
| 5. #20295091 | C2 | semidirect |
| 6. #20294992 | C2 | semidirect |
| 7. #20294989 | C2 | semidirect |
| 8. #20294982 | C2 | semidirect |
| 9. #424×C109 | C2 | semidirect |
| 14. C2×#13182012 | C22 | semidirect |
| 19. C2×C8×D109 | C22 | semidirect |
| 26. #16812611 | C22 | semidirect |
| 27. #16812610 | C22 | semidirect |
| 28. C4×#11724784 | C22 | semidirect |
| 32. C4⋊C8×C109 | C22 | semidirect |
| 48. C2×#11724784 | D4 | semidirect |
| 101. C2×D109 | #131 | semidirect |
| 114. C109 | #2929 | semidirect |
| 120. #424 | D109 | semidirect |
| 142. C4⋊C8 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812707 | 2 |
| C22×C8×D109 | 2 |
| #20295538 | 2 |
| #20295096 | 2 |
| #20295091 | 2 |
| #20294992 | 2 |
| #20294989 | 2 |
| #20294982 | 2 |
| #424×C109 | 2 |
| #2929 | 109 |