Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. C2×#16812753 | C2 | semidirect |
| 3. C2×C8×#89137 | C2 | semidirect |
| 5. (C2×#89137)⋊C8 | C2 | semidirect |
| 6. (C2×#89137)⋊C8 | C2 | semidirect |
| 8. C2×#13182039 | C4 | semidirect |
| 11. C2×#13182038 | C4 | semidirect |
| 23. C22⋊#11724784 | C4 | semidirect |
| 24. #16812611 | C4 | semidirect |
| 25. #16812611 | C4 | semidirect |
| 26. C22⋊C8×C109 | C4 | semidirect |
| 73. C2×#89137 | M16 | semidirect |
| 93. #11724786 | C22⋊C4 | semidirect |
| 127. C109 | #1753 | semidirect |
| 150. C22⋊C8 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D109⋊M16 | 2 |
| C2×#16812753 | 2 |
| C2×C8×#89137 | 2 |
| C4×C22⋊#89137 | 2 |
| (C2×#89137)⋊C8 | 2 |
| C22⋊C8×D109 | 2 |
| #1753 | 109 |