Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1008 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 242 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×#13182039 | C2 | semidirect |
| 2. #20295997 | C2 | direct (N × H) |
| 3. C2×#16812756 | C2 | semidirect |
| 4. C2×C22⋊#11724786 | C2 | semidirect |
| 7. C2×#13182039 | C22 | semidirect |
| 8. C22×#11724786 | C22 | semidirect |
| 9. #16812756 | C22 | semidirect |
| 10. C22⋊#11724786 | C22 | semidirect |
| 23. C2×#11724786 | C23 | semidirect |
| 54. C23×C109 | M16 | semidirect |
| 66. C22×D109 | M16 | semidirect |
| 94. C22×C109 | C2×M16 | semidirect |
| 104. C2×D109 | C2×M16 | semidirect |
| 111. C2×C109 | #407 | semidirect |
| 118. C109 | C2×#407 | semidirect |
| 184. C23 | #13182039 | semidirect |
| 221. C22 | C2×#13182039 | semidirect |
| 231. C2 | #20295997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182039 | 2 |
| #20295997 | 2 |
| C2×#16812756 | 2 |
| C2×C22⋊#11724786 | 2 |
| C23×C4×D109 | 2 |
| C2×#407 | 109 |