Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
242 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C71 | C2×D4 |
| commutator | C2×C4 | C22×C8×C71 |
| Frattini, cosocle | C4×C8 | C23×C71 |
| socle | C22×C71 | C8×D4 |
| prime radical | C2×D8×C71 | C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C71 ◁ C4×C16×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C71×#2169 | C2 | semidirect |
| 3. C71×#1370 | C2 | semidirect |
| 4. C71×D4⋊C16 | C2 | semidirect |
| 5. C8×C16×C71 | C2 | semidirect |
| 48. C16×C71 | D8 | semidirect |
| 62. C8×C71 | M32 | semidirect |
| 75. #12039 | C71 | direct (N × H) |
| 80. #2169 | C2×C71 | semidirect |
| 82. #1370 | C2×C71 | semidirect |
| 83. D4⋊C16 | C2×C71 | semidirect |
| 84. C8×C16 | C2×C71 | semidirect |
| 85. C71 | #12039 | direct (N × H) |
| 128. C16 | D8×C71 | semidirect |
| 142. C8 | M32×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2169 | 2 |
| C8×D8×C71 | 2 |
| C71×#1370 | 2 |
| C71×D4⋊C16 | 2 |
| C8×C16×C71 | 2 |
| #12039 | 71 |