Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
| 13. #16812756 | C4 | semidirect |
| 14. C22⋊#11724786 | C4 | semidirect |
| 19. C2×#13182013 | C4 | semidirect |
| 20. C2×#13182012 | C4 | semidirect |
| 21. C2×#13182012 | C4 | semidirect |
| 26. C2×M16×C109 | C4 | semidirect |
| 75. C2×#89137 | M16 | semidirect |
| 97. C8×C109 | C22⋊C4 | semidirect |
| 99. #11724784 | C22⋊C4 | semidirect |
| 129. C109 | #1753 | semidirect |
| 143. C2×M16 | #89137 | semidirect |
| 228. C8 | C22⋊#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊(C22⋊C8) | 2 |
| C2×#16812753 | 2 |
| C2×C8×#89137 | 2 |
| C4×C22⋊#89137 | 2 |
| (C2×#89137)⋊C8 | 2 |
| C2×M16×D109 | 2 |
| #1753 | 109 |