Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 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. C2×#16812724 | C2 | semidirect |
| 2. C22×#13182016 | C2 | semidirect |
| 3. #20295590 | C2 | semidirect |
| 4. #20295171 | C2 | semidirect |
| 5. #20295165 | C2 | semidirect |
| 6. #20295035 | C2 | semidirect |
| 7. #20295022 | C2 | semidirect |
| 8. #20294993 | C2 | semidirect |
| 9. C2×2−1+4×C109 | C2 | semidirect |
| 23. #16812623 | C22 | semidirect |
| 24. #16812623 | C22 | semidirect |
| 25. #16812620 | C22 | semidirect |
| 26. C22⋊#11724784 | C22 | semidirect |
| 33. C2×#41×C109 | C22 | semidirect |
| 36. C22×Q8×C109 | C22 | semidirect |
| 61. #41×C109 | D4 | semidirect |
| 69. C2×Q8×C109 | D4 | semidirect |
| 146. C109 | #3010 | semidirect |
| 147. C2×2−1+4 | D109 | semidirect |
| 162. C2×#41 | C2×D109 | semidirect |
| 165. C22×Q8 | C2×D109 | semidirect |
| 191. #41 | C22⋊D109 | semidirect |
| 199. C2×Q8 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812724 | 2 |
| C22×#13182016 | 2 |
| #20295590 | 2 |
| #20295171 | 2 |
| #20295165 | 2 |
| #20295035 | 2 |
| #20295022 | 2 |
| #20294993 | 2 |
| C2×2−1+4×C109 | 2 |
| #3010 | 109 |