Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
372 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 94 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. D109⋊(C4⋊C8) | C2 | semidirect |
| 3. #20295972 | C2 | semidirect |
| 4. #20295899 | C2 | semidirect |
| 15. C4×D436 | C4 | semidirect |
| 16. D4×Dic109 | C4 | semidirect |
| 17. #16812661 | C4 | semidirect |
| 23. C4×D4×C109 | C4 | semidirect |
| 74. D4×C109 | C4⋊C4 | semidirect |
| 88. D436 | C4⋊C4 | semidirect |
| 122. C4×C109 | #102 | semidirect |
| 127. Dic109 | #102 | semidirect |
| 140. C109 | #1802 | semidirect |
| 154. C4×D4 | #89137 | semidirect |
| 215. D4 | C4⋊#89137 | semidirect |
| 267. C4 | #16812761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊(C4⋊C8) | 2 |
| C2×#16812761 | 2 |
| #20295972 | 2 |
| #20295899 | 2 |
| C4×D4×D109 | 2 |
| #1802 | 109 |