Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
176 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C73 |
| prime radical | C2×D16×C73 | C22 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ C4×C8×C73 ◁ C4×C16×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C73×#2252 | C2 | semidirect |
| 3. C73×#1423 | C2 | semidirect |
| 4. C73×C4⋊C32 | C2 | semidirect |
| 19. D16×C73 | Q8 | semidirect |
| 66. #13703 | C73 | direct (N × H) |
| 71. #2252 | C2×C73 | semidirect |
| 73. #1423 | C2×C73 | semidirect |
| 74. C4⋊C32 | C2×C73 | semidirect |
| 76. C73 | #13703 | direct (N × H) |
| 90. D16 | Q8×C73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#2252 | 2 |
| C4×D16×C73 | 2 |
| C73×#1423 | 2 |
| C73×C4⋊C32 | 2 |
| C73×#1415 | 2 |
| #13703 | 73 |