Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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. #20295134 | C2 | semidirect |
| 4. #20295133 | C2 | semidirect |
| 5. #20295132 | C2 | semidirect |
| 6. C4×#13182019 | C2 | semidirect |
| 7. #20295118 | C2 | semidirect |
| 11. #441×C109 | C2 | semidirect |
| 15. Q16×D109 | C4 | semidirect |
| 109. C109 | #2950 | semidirect |
| 115. #441 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D109 | 2 |
| #20295502 | 2 |
| #20295134 | 2 |
| #20295133 | 2 |
| #20295132 | 2 |
| C4×#13182019 | 2 |
| #20295118 | 2 |
| #20295061 | 2 |
| #20295033 | 2 |
| #20294983 | 2 |
| #441×C109 | 2 |
| #2950 | 109 |