Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
528 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22601192 | C2 | semidirect |
| 2. #22590614 | C2 | semidirect |
| 3. #22590476 | C2 | semidirect |
| 4. #22590474 | C2 | semidirect |
| 5. C16×Dic142 | C2 | semidirect |
| 8. C71×#2252 | C2 | semidirect |
| 36. D1136 | Q8 | semidirect |
| 58. D568 | C2×Q8 | semidirect |
| 75. C16×C71 | C2×Q8 | semidirect |
| 90. Dic142 | D16 | semidirect |
| 114. #2252 | D71 | semidirect |
| 120. C71 | Q8×D16 | semidirect |
| 187. C16 | Q8×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601192 | 2 |
| #22590614 | 2 |
| #22590476 | 2 |
| #22590474 | 2 |
| C16×Dic142 | 2 |
| C4×D1136 | 2 |
| #22590186 | 2 |
| C71×#2252 | 2 |
| Q8×D16 | 71 |