Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
250 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#17985838 | C2 | semidirect |
| 2. #22590593 | C2 | semidirect |
| 4. C4×C32×C71 | C2 | semidirect |
| 27. C32×C71 | D4 | semidirect |
| 58. C4×C71 | SD64 | semidirect |
| 69. C4×C32 | D71 | semidirect |
| 70. C71 | #13727 | semidirect |
| 93. C32 | D284 | semidirect |
| 125. C4 | #17985838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985838 | 2 |
| #22590593 | 2 |
| #22590590 | 2 |
| C4×C32×C71 | 2 |
| #13727 | 71 |