Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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. #20297351 | C2 | semidirect |
| 2. #20297332 | C2 | semidirect |
| 3. #20297329 | C2 | semidirect |
| 4. #20297292 | C2 | semidirect |
| 5. #20297232 | C2 | semidirect |
| 6. #20297222 | C2 | semidirect |
| 7. #104×C223 | C2 | semidirect |
| 63. C223 | #454 | semidirect |
| 70. #104 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297351 | 2 |
| #20297332 | 2 |
| #20297329 | 2 |
| #20297292 | 2 |
| #20297232 | 2 |
| #20297222 | 2 |
| #104×C223 | 2 |
| #454 | 223 |