Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4×C4⋊Dic109 | C2 | semidirect |
| 4. #20294789 | C2 | semidirect |
| 5. C2×C4×C8×C109 | C2 | semidirect |
| 9. C4×D436 | C4 | semidirect |
| 14. #16812621 | C4 | direct (N × H) |
| 32. C4⋊Dic109 | C2×C4 | semidirect |
| 40. C2×C8×C109 | C2×C4 | semidirect |
| 66. D436 | C42 | semidirect |
| 80. C4×C109 | #102 | semidirect |
| 93. C109 | C4×#102 | semidirect |
| 96. C2×C4×C8 | D109 | semidirect |
| 127. C2×C8 | C4×D109 | semidirect |
| 175. C4 | #16812621 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D436 | 2 |
| C2×#16812621 | 2 |
| C4×C4⋊Dic109 | 2 |
| #20294789 | 2 |
| C2×C4×C8×C109 | 2 |
| C4×#102 | 109 |