Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. M16×D223 | C2 | semidirect |
| 3. C42×D223 | C2 | semidirect |
| 4. #20297232 | C2 | semidirect |
| 5. #20297231 | C2 | semidirect |
| 6. #20297230 | C2 | semidirect |
| 7. #104×C223 | C2 | semidirect |
| 8. #16813171 | C4 | semidirect |
| 12. #16813169 | C4 | semidirect |
| 13. Q8×D223 | C4 | semidirect |
| 15. D4×D223 | C4 | semidirect |
| 19. #16813154 | C22 | semidirect |
| 23. C4×Dic223 | C22 | semidirect |
| 25. M16×C223 | C22 | semidirect |
| 26. C42×C223 | C22 | semidirect |
| 30. Dic446 | C2×C4 | semidirect |
| 32. D892 | C2×C4 | semidirect |
| 48. Q8×C223 | C2×C4 | semidirect |
| 50. D4×C223 | C2×C4 | semidirect |
| 75. D223 | #104 | direct (N × H) |
| 76. C223 | C2×#104 | semidirect |
| 84. #104 | D223 | direct (N × H) |
| 99. M16 | C2×D223 | semidirect |
| 103. C42 | C2×D223 | semidirect |
| 108. Q8 | C4×D223 | semidirect |
| 115. D4 | C4×D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D223 | 2 |
| M16×D223 | 2 |
| C42×D223 | 2 |
| #20297232 | 2 |
| #20297231 | 2 |
| #20297230 | 2 |
| #104×C223 | 2 |
| C2×#104 | 223 |