Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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×D109⋊M16 | C2 | semidirect |
| 2. C2×#16812778 | C2 | semidirect |
| 3. #20296025 | C2 | direct (N × H) |
| 4. C2×#16812764 | C2 | semidirect |
| 6. C2×#13182039 | C22 | semidirect |
| 8. D109⋊M16 | C22 | semidirect |
| 12. #16812778 | C22 | semidirect |
| 15. C2×C4×#89137 | C22 | semidirect |
| 16. #16812764 | C22 | semidirect |
| 21. C2×#13182030 | C4 | semidirect |
| 22. C2×#13182030 | C4 | semidirect |
| 26. C22×D436 | C4 | semidirect |
| 29. C22×Q8×C109 | C4 | semidirect |
| 32. #13182039 | C23 | semidirect |
| 39. C4×#89137 | C23 | semidirect |
| 50. #13182030 | C2×C4 | semidirect |
| 59. C2×D436 | C2×C4 | semidirect |
| 76. C2×Q8×C109 | C2×C4 | semidirect |
| 145. C2×C109 | #421 | semidirect |
| 152. C109 | C2×#421 | semidirect |
| 166. C22×Q8 | #89137 | semidirect |
| 197. C2×Q8 | C2×#89137 | semidirect |
| 301. C2 | #20296025 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D109⋊M16 | 2 |
| C2×#16812778 | 2 |
| #20296025 | 2 |
| C2×#16812764 | 2 |
| C22×#13182030 | 2 |
| C2×#421 | 109 |