Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 184 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. #22624846 | C2 | semidirect |
| 3. #22624844 | C2 | semidirect |
| 38. C8×D73 | C16 | semidirect |
| 59. C8×C73 | C2×C16 | semidirect |
| 61. #10596831 | C2×C16 | semidirect |
| 77. D73 | #1312 | semidirect |
| 82. C73 | C2×#1312 | semidirect |
| 140. C8 | #14556664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556664 | 2 |
| #22624846 | 2 |
| #22624844 | 2 |
| C82×D73 | 2 |
| C2×#1312 | 73 |