Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C2×#16812753 | C2 | semidirect |
| 4. C2×C8×#89137 | C2 | semidirect |
| 5. (C2×#89137)⋊C8 | C2 | semidirect |
| 6. (C2×#89137)⋊C8 | C2 | semidirect |
| 16. #16812756 | C4 | semidirect |
| 17. C22⋊#11724786 | C4 | semidirect |
| 23. C22⋊#11724784 | C4 | semidirect |
| 24. #16812611 | C4 | semidirect |
| 25. #16812611 | C4 | semidirect |
| 26. C22⋊C8×C109 | C4 | semidirect |
| 126. C109 | #1750 | 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×#16812778 | 2 |
| D109⋊(C22⋊C8) | 2 |
| C2×#16812753 | 2 |
| C2×C8×#89137 | 2 |
| (C2×#89137)⋊C8 | 2 |
| C22⋊C8×D109 | 2 |
| #1750 | 109 |