Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
220 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #102 |
| commutator | C8 | C22×C4×C17 |
| Frattini, cosocle | C2×C8 | C23×C17 |
| socle | C2×C17 | C2×#102 |
| prime radical | C2×C17×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C22×C8×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C17×M32 | C2 | semidirect |
| 3. C2×C17×#108 | C2 | semidirect |
| 4. C17×#362 | C2 | semidirect |
| 5. C17×#361 | C2 | semidirect |
| 68. #2148 | C17 | direct (N × H) |
| 81. C2×M32 | C2×C17 | semidirect |
| 82. C2×#108 | C2×C17 | semidirect |
| 83. #362 | C2×C17 | semidirect |
| 84. #361 | C2×C17 | semidirect |
| 105. C17 | #2148 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#135 | 2 |
| C2×C17×M32 | 2 |
| C2×C17×#108 | 2 |
| C17×#362 | 2 |
| C17×#361 | 2 |
| #2148 | 17 |