Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13182016 | C2 | semidirect |
| 3. #20295504 | C2 | semidirect |
| 4. #20295250 | C2 | semidirect |
| 5. #20295224 | C2 | semidirect |
| 6. #20295054 | C2 | semidirect |
| 7. #20295032 | C2 | semidirect |
| 8. #20295022 | C2 | semidirect |
| 9. C2×#137×C109 | C2 | semidirect |
| 19. Q8×Dic109 | C22 | semidirect |
| 23. #16812628 | C22 | semidirect |
| 24. #16812623 | C22 | semidirect |
| 26. #16812620 | C22 | semidirect |
| 30. C2×Q16×C109 | C22 | semidirect |
| 31. C2×SD16×C109 | C22 | semidirect |
| 55. C2×Q8×C109 | D4 | semidirect |
| 117. C109 | #3043 | semidirect |
| 118. C2×#137 | D109 | semidirect |
| 131. C2×Q16 | C2×D109 | semidirect |
| 134. C2×SD16 | C2×D109 | semidirect |
| 155. C2×Q8 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182016 | 2 |
| #20295590 | 2 |
| #20295504 | 2 |
| #20295250 | 2 |
| #20295224 | 2 |
| #20295054 | 2 |
| #20295032 | 2 |
| #20295022 | 2 |
| C2×#137×C109 | 2 |
| #3043 | 109 |