Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
604 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C73×#2011 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C73×#2683 | C2 | semidirect |
| 2. C73×#2041 | C2 | semidirect |
| 4. C73×#1271 | C2 | semidirect |
| 5. C73×#1270 | C2 | semidirect |
| 86. C4⋊C4×C73 | D8 | semidirect |
| 155. #7738 | C73 | direct (N × H) |
| 163. #2683 | C2×C73 | semidirect |
| 164. #2041 | C2×C73 | semidirect |
| 166. #1271 | C2×C73 | semidirect |
| 167. #1270 | C2×C73 | semidirect |
| 168. C73 | #7738 | direct (N × H) |
| 249. C4⋊C4 | D8×C73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#2683 | 2 |
| C73×#2041 | 2 |
| C73×#2011 | 2 |
| C73×#1271 | 2 |
| C73×#1270 | 2 |
| #7738 | 73 |