Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
552 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 186 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. C22×#13182038 | C2 | semidirect |
| 3. #20296059 | C2 | direct (N × H) |
| 4. C2×#16812766 | C2 | semidirect |
| 5. C2×#16812756 | C2 | semidirect |
| 6. C2×C22⋊#11724786 | C2 | semidirect |
| 7. C2×C4×#11724786 | C2 | semidirect |
| 10. C2×#13182039 | C22 | semidirect |
| 12. C2×#13182038 | C22 | semidirect |
| 17. #16812766 | C22 | semidirect |
| 18. #16812756 | C22 | semidirect |
| 19. C22⋊#11724786 | C22 | semidirect |
| 20. C4×#11724786 | C22 | semidirect |
| 35. C2×#11724786 | D4 | semidirect |
| 80. C2×Dic109 | M16 | semidirect |
| 93. #11724786 | C2×D4 | semidirect |
| 110. Dic109 | C2×M16 | semidirect |
| 114. C2×C109 | #436 | semidirect |
| 120. C109 | C2×#436 | semidirect |
| 235. C2 | #20296059 | 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 |
| C22×#13182038 | 2 |
| #20296059 | 2 |
| C2×#16812766 | 2 |
| C2×#16812756 | 2 |
| C2×C22⋊#11724786 | 2 |
| C2×C4×#11724786 | 2 |
| C2×#16812659 | 2 |
| C2×#436 | 109 |