Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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. C22×#13182004 | C2 | semidirect |
| 2. C2×C16×D109 | C2 | semidirect |
| 4. #20294844 | C2 | semidirect |
| 5. #20294805 | C2 | semidirect |
| 6. C16×Dic109 | C2 | semidirect |
| 7. C22⋊C16×C109 | C2 | semidirect |
| 32. #13182004 | D4 | semidirect |
| 46. C22⋊D109 | C16 | semidirect |
| 59. C22×C109 | C2×C16 | semidirect |
| 63. C2×D109 | C2×C16 | semidirect |
| 69. Dic109 | C2×C16 | semidirect |
| 76. C109 | D4×C16 | semidirect |
| 82. C22⋊C16 | D109 | semidirect |
| 138. C22 | C16×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182004 | 2 |
| C2×C16×D109 | 2 |
| C8×C22⋊D109 | 2 |
| #20294844 | 2 |
| #20294805 | 2 |
| C16×Dic109 | 2 |
| C22⋊C16×C109 | 2 |
| D4×C16 | 109 |