Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 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. #10625160 | C2 | semidirect |
| 2. #10625120 | C2 | semidirect |
| 3. #10625079 | C2 | semidirect |
| 4. #10625045 | C2 | semidirect |
| 5. C23×#104 | C2 | semidirect |
| 6. #10625005 | C2 | semidirect |
| 7. #10624987 | C2 | semidirect |
| 17. C2×D92 | C22 | semidirect |
| 18. M16×C23 | C22 | semidirect |
| 19. C42×C23 | C22 | semidirect |
| 22. #67267 | C22 | semidirect |
| 28. Q8×C23 | D4 | semidirect |
| 30. D4×C23 | D4 | semidirect |
| 42. D92 | D4 | semidirect |
| 45. Dic46 | D4 | semidirect |
| 73. #104 | D23 | semidirect |
| 75. C23 | #453 | semidirect |
| 91. M16 | C2×D23 | semidirect |
| 92. C42 | C2×D23 | semidirect |
| 97. Q8 | D92 | semidirect |
| 108. D4 | D92 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10625160 | 2 |
| #10625120 | 2 |
| #10625079 | 2 |
| #10625045 | 2 |
| C23×#104 | 2 |
| #10625005 | 2 |
| #10624987 | 2 |
| #453 | 23 |