Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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. #20295402 | C2 | semidirect |
| 2. #20295222 | C2 | semidirect |
| 3. #20295218 | C2 | semidirect |
| 4. #20295103 | C2 | semidirect |
| 5. #20294776 | C2 | semidirect |
| 6. #20294769 | C2 | semidirect |
| 7. #331×C109 | C2 | semidirect |
| 69. #11724784 | D8 | semidirect |
| 93. C109 | #1687 | semidirect |
| 100. #331 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295402 | 2 |
| #20295222 | 2 |
| #20295218 | 2 |
| #20295103 | 2 |
| #20294776 | 2 |
| #20294769 | 2 |
| #331×C109 | 2 |
| #1687 | 109 |