Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20297352 | C2 | semidirect |
| 2. #20297336 | C2 | semidirect |
| 3. #20297335 | C2 | semidirect |
| 4. #20297327 | C2 | semidirect |
| 5. #20297326 | C2 | semidirect |
| 6. Q16×D223 | C2 | semidirect |
| 7. #20297310 | C2 | semidirect |
| 8. C2×Q16×C223 | C2 | semidirect |
| 59. C223 | #578 | semidirect |
| 67. C2×Q16 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297352 | 2 |
| #20297336 | 2 |
| #20297335 | 2 |
| #20297327 | 2 |
| #20297326 | 2 |
| Q16×D223 | 2 |
| #20297310 | 2 |
| C2×Q16×C223 | 2 |
| #578 | 223 |