Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
234 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 76 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×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| prime radical | C2×D4×C17 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#498 | C2 | semidirect |
| 3. C17×#475 | C2 | semidirect |
| 5. C17×#332 | C2 | semidirect |
| 6. C17×Q8⋊C8 | C2 | semidirect |
| 57. Q8×C17 | SD16 | semidirect |
| 74. #1651 | C17 | direct (N × H) |
| 90. #498 | C2×C17 | semidirect |
| 91. #475 | C2×C17 | semidirect |
| 93. #332 | C2×C17 | semidirect |
| 94. Q8⋊C8 | C2×C17 | semidirect |
| 117. C17 | #1651 | direct (N × H) |
| 150. Q8 | SD16×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C17 | 2 |
| C17×#498 | 2 |
| C17×#475 | 2 |
| C17×#461 | 2 |
| C17×#332 | 2 |
| C17×Q8⋊C8 | 2 |
| C17×D4⋊C8 | 2 |
| #1651 | 17 |