Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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. Q8×D568 | C2 | semidirect |
| 2. #22590615 | C2 | semidirect |
| 3. #22590478 | C2 | semidirect |
| 5. Q8×C16×C71 | C2 | semidirect |
| 22. D1136 | Q8 | direct (N × H) |
| 36. D568 | C2×Q8 | semidirect |
| 46. C16×C71 | C2×Q8 | semidirect |
| 48. Q8×C71 | D16 | semidirect |
| 77. Q8×C16 | D71 | semidirect |
| 79. C71 | Q8×D16 | semidirect |
| 120. C16 | Q8×D71 | semidirect |
| 123. Q8 | D1136 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D568 | 2 |
| #22590615 | 2 |
| #22590478 | 2 |
| C4×D1136 | 2 |
| Q8×C16×C71 | 2 |
| Q8×D16 | 71 |